Are you polishing by hand? If so i would go with a filler heavy polish. I would clay it first, polish then wax. Here is what you could get.
Clay mit -
http://www.halfords.com/motoring/car...prep-clay-mitt
Autoglym Super Resin polish -
http://www.halfords.com/motoring/car...polish-1-litre
Wax/sealant -
http://www.halfords.com/motoring/car...otection-325ml
Should all come in under your £40 budget. The polish has a very light cut but masks swirl marks well and your car should look good.
When washing use a good wash mitt, and a drying towel as well and use the two bucket wash method