Can't help with the Midlands I'm afraid, but for anyone to the West of London I know of Black Park and Virginia Water.
Black Park is between London and Slough, adjacent to Pinewood Studios. There is a car park which charges £2.00 but you can park in one of the lay-bys (?) if there is room. It takes about 1hr 30 mins to walk around the park. The park is very well maintained (with the help of the car parking money) and the paths do not get very muddy even in the middle of Winter. Its a lovely place to go in winter because the dogs can race around in the mud in an attempt to turn themselves into Black Labs and then clean in the lake which, conveniently, is next to the car park.
I have only been to Virginia water three times since it is much further than Black Park. It is part of Windsor Great Park. The car part there costs £4.00 but, once again, you can park in lay-bys. IIRC all the paths are made of tarmac so you don't need boots. The lake is very large and the park is massive and you might even meet some corgis.