I'd be the first to admit I bought my BMW with my heart rather than head, its certainly not the cheapest way of picking your cars! That said, I'm happy as I had absolutely no illusions as to what running my car could potentially be like.
Anyways, imo,the price is too high for the mileage imo, as said though,its a major bargaining point. The lack of service history should chop £600 off it immediately as the first thing you need to do once buying it is to spend such an ammount on a decent service and discover whatever else lurks under its fine looking skin.
The thing
should be stuffed full of invoices somewhere, if not, as Fox says,it sounds to me like the previous owners been running it very much on the cheap, easily done in a BMW, many still drive quite well, even with major work required!
Using my car as an example,as I could easily stick it up for sale @ £4k if I wanted to.
My service book was'nt stamped (I'll have to look!) when I had my last service, I do have the invoice however and, it'll stay in the car, as I do for the oil service it had 6000 miles back and tyres, brakes etc etc.
Consider this, in the last 11000 miles, I serviced my car 1k & 7k back, costing me £250 & £454 respectively and thats with a detailed service history upto the point I bought it.
I could have
very easily sold the car, having not touched ,mechanically, bar a puncture (which you have no option but to get fixed I find!) after I'd done my 11k in it - giving me 12 months & 11kmiles of cheap 7 Series running - but left the new owner with a very nasty & expensive surprise after his first 1k of ownership could'nt I? Many BMW's are sold on thus, testament to the initial quality of the things that they take such neglect ultimately leaving some unfortunate purchaser crying.
That could very well be the case with this 540i, these bells are getting louder!
Your on a budget, which to an extent , I was I suppose.
Forget the V8 and look at a 523 / 528.
Caveat emptor my friend.