Quick count...
Wheels will be £150, tyres £40, brakes... depends what sort (caliper, canti, disc, v) but say £50, another £50 if you need levers as well and stick in £20 for cables. That's £310 in parts. Add £100 for a couple of hours to put it all together and, let's say £40 for "sundries" like swapping out knackered bolts, greasing cranks etc,
That's £450 and most of the way to a nice bike and is probably why your LBS said it wasn't worth it.
A bike repair service would normally, IMO, be swapping out any one of those items. You are looking for a rebuild service, not a repair service!
Then again, if the bike has non-monetary value to you, then that's all irrelevant.
I went through the same with my old bike, first place I went into didn't even want to sell me a BB as they reckoned the bike wasn't worth it. Luckily, I persisted and I've had some fun getting my old bike back on the road for the price of a new BB and a pair of tyres (so far

).