Well garages way up the price - time involved / Versus labour charge, Plus parts - some garages now charging well over £100 an hour plus VAT
There is talk of a batch of badly made soft valve seats ..
which may be the issue.
https://www.youtube.com/watch?v=S6V29CuN_Y8New engine for garage may be cheaper than cylinder head overhaul when charged to you, cost and effect and warranty comes into it as well .. what they believe is worth there while and they don't want come backs.
You've not said your mileage
You have a lot of things to factor in .. like is the wetbelt due, so new parts needed anyway.
To do a cylinder head overhaul, a garage would have to take the head off and send it to a machine shop for further work .. skim , valve seats... that's why engine may be cheaper.
if you did it yourself it would be a totally different scenario and would indeed work out cheaper.
Note: if it was the piston ring and bore wear "unlikely" .. causing this, then there are plenty of used short engines ( basic block minus pistons, minus crank )on ebay
very cheap £120 ish .. because the wetbelts have totalled a lot of them, owner bought whole engine and sold the sound blocks
Cylinder heads are a dodgy buy when used .. and must come with a cam carrier
You'll have to way up the pros and cons yourself
all the best.mark