Elizabeth - is there a reason why you have not let grass grow beneath the trees? Is it like an orchard? You could try growing comfrey, though if the area is shady it might not do so well. The variety 'Bocking 14' does not self seed, so won't seed into your lawn, but it will bulk up and spread eventually through its roots. Comfrey is great for bees and rich in potash and other minerals. Once a year you could chop down the foliage and leave it to rot into the soil to fertilise the trees, or make a comfrey solution to feed to flowering plants and tomato/chilli/aubergine crops to improve flowering potential and fruit set.
Gill - it sounds like you have heavy clay soil. I'm afraid it's going to be backbreaking! Just dig over a small patch at a time, incoporating as much organic matter (in the form of home-made compost or well-rotted horse manure) as you can get your hands on. Grow deep-rooted plants such as potatoes, which will help to break up the soil. A deep-rooted green manure such as grazing rye will also help. Here is more information on improving soil and sowing grazing rye:
http://www.gardenersworld.com/how-to/projects/soil-improve/
http://www.gardenersworld.com/how-to/projects/soil-improve-green-manure/
Des Caldwell - That sounds terrible! Yes, you can improve heavy clay soil in the manner you suggested, but if the builders didn't do a very good job initially, it may be that you actually have a lot of subsoil in the mix, which is very low in nutrients and not suitable for growing things in. Is the lawn not growing well? You could try working with what you've got: aerating, scarifying and feeding your lawn (info here: http://www.gardenersworld.com/how-to/projects/category/lawn-care/), and perhaps sprinkling a mixture of sharp sand, topsoil and grass seed over the lawn. This will probably need doing every year if you want to improve the state of the lawn in the long term, but its success depends on how bad it is now...
Melanie - I would sow field beans now, if you are in the south of the UK you might get away with grazing rye, but field beans can be sown until November. They also have deep roots, which are excellent for breaking up heavy soil. You could mulch with a combination of compost or well-rotted manure, which would help aerate the soil and separate its heavy particles, but I'd personally opt for sowing a green manure now (easier), then grow potatoes next year. These will continue to break up the soil and should make it more manageable in the future. You could follow the potato crop with a mulch of compost or horse manure in late summer, or just sow another green manure and leave it til the following spring.
June - there are so many vareities to choose from. here is a list from allotment.org.uk: http://www.allotment.org.uk/vegetable/potato/potato-flavour-type.php
Kate