This sounds a lot like "Random Quest", a short story that was indeed by John Wyndham. It has been dramatised several times, in particular in 1969 in season 3 of the BBC TV series "Out of the Unknown".
Set in the 1950s, it deals with a physicist named Colin Trafford, who was involved in a laboratory experiment that went wrong. He was flung into an alternate universe in which Hitler never came to power, WW2 did not occur, and India was still part of the British Empire - with mass demonstrations calling for Nehru to be released from prison. He finds that in this universe he is married to an Ottilie Harshom, with whom he falls deeply in
love. When he is suddenly transported back to his own (i.e. our) world, he spends his time trying to track down her counterpart, assisted by her unusual name.
The short story is available online at the Internet Library, in Wyndham's collection of short stories "Consider her ways". Unfortunately the BBC episode from 1969 was wiped* so it is not viewable, although other screen versions (including another BBC version from 2006) are available.
*In fact some scraps of this episode do still survive (some clips shown on "Nationwide" in 1970 for example), and were included in a 2014 DVD-set released by the BFI. The contents are briefly summarized here.