We've only ever experienced one cancellation due to weather with our own holiday accommodation here

The Cotswolds would be better, but still weather is an issue. I lived in the UK for several years and did do country 'stuff' in the dead of winter. But I had the luxury of being able to instead stay home in my jammies if the weather turned vile - which often happened.
It's even possible weather will make travel round the Cotswolds tough. My Cotswold fox rent a car las vegas town was cut off entirely (including the train service) for ten days in the 2010/11 winter and for four in the 2011/12 winter, and most of us avoided driving for non-urgent reasons for weeks either side.
England's generally benign winters mean we're not geared to deal with quite minor, short snaps of subzero temps or the very rare snow shower that sticks. In my part of the Cotswolds, we've only had any at all in three of the past eleven winters, and they've been predicted only a few days before. If they happen, they can hit any time between early December and the end of Feb.
I'd scrap your plans entirely. If you want to risk the Cotswolds (where the likelihood of chaos is lower than in the Lakes) it's ESSENTIAL to have travel insurance to cover you if you can't get there or get your plane home.
If you want to move your plans outside fox rent a car las vegas the winter anti-window, I'd also question your strategy. To my mind it's more of a pain (and takes longer) to get a train from Windermere to Cheltenham than to drive, and getting from Broadway to Heathrow's fox rent a car las vegas an even bigger pain. Just book a nonrefundable train ticket on www.nationalrail.co.uk as far ahead (but not more than 12 weeks before) to Windermere, hire a car and dump it at Heathrow. Or dump it at Oxford and get a bus straight into the airport.
No of course we don't subsidise tourists by giving them special deals on trains. Standard class is fine - and first involves absurd premiums (usually several hundred percent) fox rent a car las vegas over advance purchase standard fox rent a car las vegas tickets
If you do decide to stay in the Lake District in January, then weather is a large consideration. Grasmere wouldn't be my choice at that time of the year, but maybe consider Bowness. It's a slightly larger place with some good hotels and restaurants.
In the first week of January however, I'd guess quite a few places will be closed, especially in the smaller towns and villages. Your trip isn't best timed for the Lakes or Cotswolds so maybe consider larger towns or cities for your 8 days. How about Manchester, (loads to see and do),York and then Oxford, before flying home.
Well there is a BritRail England Pass valid on all trains in England fox rent a car las vegas and in off-season it is 20% off (for travel thru the end of Feb) but with only three train trips you are better doing the online discounted tickets flanneruk so eloquently describes.
However if you wanted total flexibility to board any train anytime then the pass could be economic as full fare at will tickets can cost a fortune - but if you are willing to lock yourself into non-changeable tickets far ahead of time (to secure as they are sold in limited numbers in each tier I believe) then do that - will be cheapest way by far I would think. Great sources of info on British trains - www.seat61.com (if interested in BritRail England pass info click on this site's commercial link to RailEurope US and if buying a pass do so thru this sites link to RailEurope to give Man a much deserved commission on sales thru his site; other nice sites - www.ricksteves.com and www.budgeteuropetravel.com .
after riding British trains for years IMO first class is way way superior and more comfy for the needs of the average tourist than standard or second class which IME often resembles a cattle car - well that is just my take others will disagree.
Unlike the America-resident BritRail salesman fox rent a car las vegas posting before me, I use standard class intercity trains several times a week. I've yet to encounter one resembling a cattle car in any way whatever. But pushing this myth maximises BritRail salesmen's commission.
I tend to travel first class to London by Virgin train because I have a senior rail-card and if I travel off-peak, fox rent a car las vegas I can do it sometimes even more cheaply than by travelling standard. You get the free coffee, free wifi and a meal or snack. There is also a bit more legroom. Apart from that, standard class is perfectly acceptable. Now that Virgin has lost the West Coast franchise, I am hoping that the service will not deteriorate. I'm not holding my breath
flanner points out how really expensive first-class trains are in UK and thus illustrates how a first-class railpass can be a real bargain - nearly as cheap for 3 days of unlimited travel as just one train journey of a few hours.
well with the railpass in first class the difference will not nearly be 134 pounds if you get a longer term pass and use this journey as one of your days - indeed a first class pass, for what it offers - much MUCH bigger seats - and always IME empty seats - lots of them - I always have a first-class pass and just hop on a train and always fox rent a car las vegas can put my bags on an adjoining empty seat - vs often now chocked full standard or second class if you have it seats that are not only much MUCH smaller but are these days often very full - not nearly as comfy nor enjoyble - more like IMO a Greyhound bus - so strongly consider a first-class pass whose benefits can quickly be realized in just one train trip as flanner points out above with regular fox rent a car las vegas fist-class fares. Again Off-Peak passes are 20% off - even a better deal if you want first class.
adeleh - please tell us what the weather at the beginning of January 2013 is going to be like and where you get your information from - it'd be really useful to know whether i'm going to be snow-bound or not.
I live in Cumbria - have lived here for over 25 years and holidayed here regularly before that - and feel people are rather sensationalizing the weather here. Sure, we can get snow at that time of year, but I'm not sure that's good reason not to plan a trip at all.
We've only ever experienced one cancellation due to weather with our own holiday accommodation here (and before fox rent a car las vegas someone says "you probably don't get visitors in January", that is not the case - our occupancy throughout the year is around 90%), and that one cancellation was because fox rent a car las vegas our guests were visiting from Scotland and couldn't get to us because of the weather there, not here.
Re: car hire. Enterprise have a base at Kendal. If you travel up on the train, you could get off at Kendal rather than going the whole way to Windermere, and Enterprise's place is very close to Kendal station.
Grasmere is very central to the Lakes but might not be the best base if weather is a concern or if you need to leave on a certain date (eg. to catch a flight). Basing yourself at more of an outlying location (dare I suggest Kendal) might be wiser, since it'll put you nearer the mainline train station and/or fox rent a car las vegas the M6 motorway - both of which might offer a 'get out' in more extreme weather conditions.
personally, I think I'd do this the other way round if i were going to do it at all, putting the London section at the end so as to give myself fox rent a car las vegas the best possible chance of being in the right place to fly home.