First & foremost I must say that I have not seen the car..........It may be a gem with a small mark & a prior keeper may have forgotten to get the book stamped, however, I would comment as follows :
Re dealer visit checks unless you have a dealer contact It can be a bit hit & miss calling dealers first. IMO the easiset thing to do is to call BMW UK customer services premium number, (I think details are in my buyers guide- if not then look at the bmw uk website under customer service), to get info on all dealer visits & dates, then call dealers to find more info.
Obviously HPI or suitable similar check would be a must if still happy after the above,(I think RAC checks cover same as HPI but are cheaper).
Ideally prior to calling it would make sense to ask seller to give specific stamp details to cover Inspection type, dealer name & mileage & date for each.
The terminology in the listing that refers to a slight mark to the bumper would concern me.
Nothing wrong with buying any car needing work as long as it's crystal clear what you are buying & cost of car plus work doesnt exceed what you'd get for it.
Looking at sellers past transactions he/she is not a total stranger to vehicle related listings. The listing doesnt scream private sale with seller name & address on V5 but I may be wrong of course.
Is it a business or private sale ?
How did seller accquire the car ?
Has a quote been given for the work to the nearside front & if so any reason why not sorted prior to sale ?
Any undisclosed defects ?
Any other known damage or body repair(s) ?
How many keys are present ?
Is seller happy to disclose last keepers details from the V5 - (if not then maybe seek an explanation IF not declaring self as a genuine trader) ?
If you get them call last keeper via directory enquiries or even send a short letter with your email & mobile - it will get there next day 1st class......(a £5 M&S gift card might work wonders).
Is any professional Inspection welcomed ?
How does he know it drives like new, (It may be a fine car but I doubt it will drive like new with @ an indicated 87k unless its had a recent suspension & bush overhaul..........thus such a statement causes me to raise an eyebrow) ?
Not for one minute saying its been clocked but bear in mind many dismiss checking for clocking on cars that are advertised with higher than average miles per year. (I've seen scruffy cars advertised with 60k miles with compressed drivers seats & a 1 owner car with over 120k that looked mint inside & out).
Developing the history again & to help check mileage - Has it got all old MOT's, (if Yes then cross check detiails with other date & mileage references before paying for the HPI check) ?
A dodgy seller will either talk bullshit or simply wont entertain such questions. Many will talk of wanting a no nonsense quick sale, suggest you are a timewaster or perhaps say someone else wants trhe car. ...Whatever the case IMO it's better to waste their time than to waste your time & money. The car you are disussing isnt being offered as a £200 bargain banger & thus you hav every reason to ask sensible Q's.
If you know your bodywork you will know all about panel gaps, loose trim, mismatches, overspray, parts with date stamp discrepancies, missing stickers, recent rivets etc, signs of airbag activation, etc etc.
OH & fwiw if it bothers you the seller can't spell properly or cant be bothered to. (My excuse is that at times I speed type - & at times badly

), however mistakes in a short & non detailed advert may set alarm bells ringing for some.
As with any listing on ebay its good to chat on the phone, however, if right noises maade then get seller to commit to what they say by ebay contact messaging. You can summarise phone call by message & simply ask them to confirm Yes No if they agree with accuracy..........this way you have things on record if things turn bad later.
Good Luck & let us know how you get on.