I'd agree with the comment that Roundup doesn't permanently kill bindweed, but yes, it knocks it back and offers some control. Once bindweed is established amongst permanent planting, it's very difficult to eradicate it, and even if you stripped out the hedge, the bindweed will still be there, no matter how hard you try to get rid of it by digging. It's one of those plants where a fraction of a piece of root left in the soil will grow again. It's also often coming from land adjacent to your own garden too,so maybe next door's garden, and unless it's tackled consistently over time wherever it's growing, the chances of eradicating it are virtually zero.
What your garden centre told you isn't strictly true - Amazon still has stocks of roundup gel and a gel wand which would be easier to use in your situation, though I've always found the gel difficult to use and not so effective as spraying. Roundup will be withdrawn in the EU for amateur use - presumably this is still true for the UK once stocks are used up. The other option is to buy a sprayer with a long wand and nozzle such as Rootblast glyphosate sprayer (Amazon has these too) which comes complete with glyphosate, and spray the growth with that by pushing it into the hedge. Glyphosate is the active ingredient in Roundup but without the additives - it kills through the green, and does not kill woody based plants, though you should try to keep the spray off the green parts of the hedge and don't use it too frequently. You can still buy glyphosate concentrate to mix up yourself so you can re-use the sprayer, but I'm not sure whether glyphosate itself will be withdrawn at some point. The best time to use these treatments is late spring as growth starts, and summer - bindweed tends to stop growing round about late July/August in the UK, it's too busy flowering to put out new growth from the base.