Well in the North there is Liverpool, York, and Newcastle, and of course Birmingham. All are hard to get on as over-subscribed (I should know I tried!). And some depend on what type of degree you did previously (assuming it's 2:1 or above).
Don't believe you can do this in service but you might be able to get the AMS scholarship (assuming cost cutting hasn't stopped them all together).
St Georges in London also do a 4 year GEP (Grad Entry Programme).
Cadetships are still being offered but apparently numbers are down to single figures per year. It was competitive enough a couple of years back when I got mine, god knows what it's like now.
Historically cadetships have always been an "enter as a civvie" thing whereby currently serving pers have had to resign current commission / resign from service, gain place at Med School on their own, last a year or two and then apply for the cadetship with no assurance they'll get a place.
There was talk last year at AMS Recruiting of at least one individual being allowed to remain in and be released from duties to study while retaining rank and pay. It was talked about as a trial but no idea if it was actually implemented or if it's even in the pipeline.
Your best bet is to drop the Recruiting team at AMS HQ a line as they're probably best placed to answer questions as the situation is changing year on year at the moment. PM if you need contact details.
I'm at Bart's and the London currently on the GEP (4 year) course. A mate of mine is army sponsored, but he applied once half way through the first year. He has been given really decent placements, heavily involved with the trauma team at the Royal London and out in the chopper etc. which most of us don't get the chance to.
Kings and Imperial also offer the 4 year course, as does warwick - which i think in the biggest one in the country. Look on UCAS, they might be able to help.
There are 16 four year courses in the UK and 28 five year courses that will accept graduates. All of these are undergraduate courses. All of them are 'good' however different teaching methods and different course structures may make some better for you than others. However, all of them are reasonably hard to get into requiring you to have reasonable academic qualifications, an understanding of work as a junior and senior doctor, experience of 'caring' as well as an ability to do well on whichever aptitude test is being used.
The RAMC has one place a year for a serving officer to attend medical school on full pay. I believe you also get SSSA and your tuition fees paid. That being said, I last heard about this before October so they may well have cut the funding by now.