The BMW N45 like nearly all BMW engines (barring the old non-vanos 4-pots) has a timing chain. It is therefore a non-serviceable item.
The chain runs along plastic guides...pretty much like any other modern engine with a chain driven top end. But concern arises if a guide should break, or tensioner fail. The chain will be loose on the one side and may jump a few teeth during start up or engine overrun.
Either way, unless its dropped a valve and damaged a piston (new engine time), I can't see how this is a £3K job. Unlike the N46, its not a valvetronic head, so far from complicated, although it may have hollow camshafts -like the N52 engine. Which might not take too kindly to opening a valve onto a piston
Another excuse for cost could be individual parts availability (cams, valves, followers etc), so maybe that £3K is for a complete new top end, as opposed to a rebuilt head (and I doubt BMW rebuild cylinder heads anyway).
Personally, considering the car's age I'd try getting BMW to repair on good will. The exception is if they feel the car has been abused in some way (overreved springs to mind, no issue if its an auto though
).