Getting images using reflected light (your prints) to match those created by transmitted light (your monitor) is a notoriously difficult task. Before you do anything else though, check your monitor. (If you're creating images that look good on a poorly set-up monitor, the chances of them looking good when printed are
extremely low).
Go here:
http://reeddesign.co.uk/testcard.htm
Check that you can see all the numbers, from 0 to 10, on both numbered lines. Also check that the black box is absolutely jet black and that the white one is pure white, with no greyness or colour cast.
With home printing, the usual cause of low-quality prints is the use of low-quality paper. (You can usually get away with using budget inks but you still need decent quality photo paper, not the muck that pound shops and supermarkets sell). It's possible that whoever supplies Boots with their prints has been trying to cut corners with their choice of papers. I've seen some impressive results from Asda though, so why try them?
Adsa's prices are here:
http://asda-photo.co.uk/about/photos.at.asda
You can take your pictures into the store (on a CD, memory stick or card), upload them and collect them later in store, or upload them and have the prints posted to you. (There are also instant self-service machines in store but the prints are more expensive).