Depends what kind of plants you are into, but I have found a lot more going on at independent garden centres than your average B&Q, prices can be fairly comparable however.
If you want some bargains then keep your eye on places like Aldi and Lidl and Wilkos as they have some bargains. Lidl were selling all sorts of clematis for £1.99 last week near me, and fruit trees for a fiver. Aldi are good for bedding plants and hanging basket plants and seeds usually. I got some asparagus from Wilko that were a lot cheaper than other places, and a couple of pear trees for less than ten pounds.
If you have a Morrisons near by I would recommend a visit, they usually have smaller plants for a couple of quid, but obviously they will take time to grow. I have had a bunch of stuff for a couple of quid from spring perenials to small shrubs to fruit bushes.
The B&Q near me have what me and OH call the 'crispy section' where they sell plants that are end of line or have drooped a bit in the hot sunshine. They will sell plants off from 10p-£2 depending on what sort of plant they are. I have had many a bargain from here. Lots of herbs, strawberries and small shrubs.
The absolute best to do for a low cost garden is bug your friends and family for anything they can spare. A lot of plants get overgrown and people will probably give you a clump with roots or some cuttings and be thankful you are taking them off their hands. You can always buy seeds too of course and grow your own.
If you have patience and can wait a couple of years for the 'established' garden look, you can do it very cheaply.
If you give us some ideas of the things you like I am sure we can give you more specific advice.