Paderborn Lippstadt Airport is indeed the nearest airport to Bielefeld but unfortunately that doesn't help as there are no direct scheduled flights from the UK. (The airport almost solely serves travellers from the immediate area seeking to get to sunshine holiday destinations).
The next nearest airport is Münster Osnabrück but, again, that only has flights to sunshine holiday destinations.
Dortmund Airport (which is the next closest) is a possibility though, if you can get to Luton (easyJet) or Stansted (Ryanair).
If you'd prefer to fly from Heathrow then you could fly to Hannover Airport with BA.
However it's Düsseldorf Airport which looks to be the most promising. As well as flights from Heathrow (BA & Eurowings) and London City (BA and FlyBe), you can also fly there from Southampton with FlyBe. Return flights in October start from under £100, with even the most expensive options not exceeding £200.
https://www.flybe.com/
There are direct trains from Düsseldorf Flughafen to Bielefeld Hbf, typically taking between 1½ and 2 hours, with single fares around €30.
https://www.bahn.com/en/view/index.shtml