I moved my two indoor bunnies outdoors 2 years ago. They absolutely LOVE it! The only problem with moving them outside is the time of year - in Winter it's not really fair as they won't have a winter coat, but this time of year is perfect. This is the time of year I moved my two out.
When keeping outdoor bunnies it's definitely very important to have 2. A single bunny outdoors will be very lonely, as you won't be able to spend as much time with them as before.
Windwhistle Warren in Gloucester and Fat Fluffs in Solihull have loads of bunnies - all very cute! They'll bond for you, and they'll come neutered and vaccinated. I think the adoption fee is around £50-60.
This hutch and run combo is a great size, and very inexpensive for what it is:
http://www.ebay.co.uk/itm/350758325427?ssPageName=STRK:MEWAX:IT&_trksid=p3984.m1438.l2649. It also doesn't take up much room so it should fit in any size garden. You'll want to get some sort of shower curtain or clear tarp to cover the top of the run to keep the rain out, and perhaps some timber panels to put inside the mesh windows for very cold weather, but it's a great hutch.
It would also be good to attach it to another run if possible, but at 6 x 2 x 2 and 6 x 4 it meets the old RWAF recommendations. They recently increased it to an 8 x 4 run, but this setup is pretty damn close.
If the garden is an odd size/shape and you can't get away with the above setup, you can get a 6 x 2 x 2 hutch (
http://www.ebay.co.uk/itm/350566100664?ssPageName=STRK:MEWAX:IT&_trksid=p3984.m1438.l2649) and connect it using the runaround tubes to a run. This is the connection kit:
http://www.runaround.co.uk/collections/frontpage/products/connection-kit-3. And here's an 8 x 4 run:
http://www.ebay.co.uk/itm/MASSIVE-R...et_Supplies_Small_Animals&hash=item35c9982b2f, or an amazing 8 x 6 run that should only cost £120 with delivery (plus he builds it for you!):
http://www.ebay.co.uk/itm/8ft-x-6ft...155?pt=LH_DefaultDomain_3&hash=item4ac6a7e273. If money isn't too much of an issue, you can get the hutch from him too and get him to build it all:
http://www.ebay.co.uk/itm/large-rab...et_Supplies_Small_Animals&hash=item4ac6b417ce.
EDIT: Here's a link to our local rescues
http://www.rabbitrehome.org.uk/centres.asp#Worcestershire