£900 is a lot but I bet it scales pretty nicely once you get to about 5.
Low volume batches come with unavoidable costs, if you are supplying the parts they still need to:
Load them onto feeders,
Program the pick and place,
Document or label up all the little odds and sods that haven't come in production ready packaging,
Get a person to manually fit those odds and sods
Buy a stencil for both sides @ ~ £140 each (unless they have a solder jet printer), I personally wouldn't be happy with one of those Chinese ones for this.
Cover the overheads of any extra processes you might expect them to be carrying out like X-Ray.
Things like
a couple of QFN devices, various TSSOP/QFN parts
are often not friendly parts to deal with in small quantities, coming poorly packaged and sometimes even with bent legs, dealing with that takes time.
That said ignore the BGA for a minute (that I don't know and cannot be bothered to lookup just how big and evil it might be) and I would expect our facility to quote a figure based on a PCB of this component count taking about 1/2 day and if you were supplying the parts the price for 5 would be quite similar to the price for one, its the setting up and tooling that costs money after all. Sadly because it is BGA and we don't have some of the toys we would like we wouldn't quote on this one, and we're busy. I'm led to believe that a lot of smaller places like ourselves are under quite a lot of pressure to undertake this work as the larger EMSs lead times and willingness to do the little stuff are becoming prohibitive. In the short term that might just mean you have to suck it up and pay a bit more, in the longer term you might find its easier to get this work done as more the smaller guys can invest in appropriate equipment with some expectation of a return.