Why did the "-re" spelling persist in the British spelling of some words?

I looked in the OED at the etymology of finger – Germanic origin; chamber – Romance origin but adopted early in Germanic languages, and Centre – Romance origin only.

The entry for finger records 49 variations in spelling until standardisation.

The entry for chamber records 123 variations in spelling until standardisation.

The entry for centre/center records 10 variations in spelling until standardisation.

In broad terms, standardisation took place in the early 18th century. At this point, spellings were fixed.

Of Centre/center, the OED notes

The prevalent spelling in the early modern period, from the 16th to the 18th centuries, was center (so in editions of major authors like Shakespeare, Milton, Pope, etc., as well as in the early dictionaries, down to all thirty editions of Bailey from 1721 to 1802). However, the technical volume of Bailey (Vol. II.), 1727–31, and the folio, 1730–6, have centre; Johnson (1755), who based his dictionary on an interleaved copy of Bailey's folio of 1730, adopted this spelling, and following Johnson's precedent, centre has become the usual form in British usage, whereas in U.S. usage center prevails.

Of chamber and finger, the OED gives the –re form as Middle English and pre-17th century.

Your answer is thus “It is like that because that is what was used and taught.”