a LOT of operators had ex London RT's (including RTLs and RTWs)...
London Transport found itself with more buses than it knew what do do with by 1954, and some of the last new RTs were put in to storage then and didn't surface until the first stages of trolleybus replacement in 1959.
The trade-off for the jig built standardisation was that the notice period to stop RT production was in months, and the decline that started after bus use in London peaked in about 1953 took LT by surprise.
The non standard Cravens bodied buses were the first to go - as has been mentioned, Dundee took a fair number as part of their tram replacement programme. While they were withdrawn in the early 70s, the standard bus to appear in comics including the 'Beano' (published by Dundee based DC Thompson) was still a roofbox RT well in to the 80s.
Most went in small numbers to independent operators (although larger independents ended up with sizeable fleets) - I can't think of many other corporation operators other than Bradford that bought RTs, likewise I don't think any Transport Holding Company / 'Tillings' or British Electric Traction group operators bought RTs directly - a few ended up with them as a result of buying out an independent, but generally didn't keep them very long and in some cases didn't operate them at all for one reason or another (as in Midland Red when they bought out Browns Blue.)
Scottish Omnibuses subsidiary Central SMT ended up with a number of RTLs after buying Laurie, Hamilton (trading as 'Chieftan') and they stayed long enough to get repainted in to Central livery. Including one where there was confusion over the chassis number and where the local licensing officer insisted on re-registering it. (photo - not my photo or account - on Flickr
here.)
A number of RTLs went to Jersey Motor Traction in the late 50s to replace mainly pre-war Leyland buses.
Ceylon has been mentioned - some were exported to South Africa, Cape Town bought a fair number (photo of one on SCT61 website
here) and there's a South African city called East London which had a few.
Abegweit Sightseeing Tours, Canada, had a fleet of RTs for sightseeing - they returned to England in 2010 (album -again not mine - on Flickr
here.
Giraffe Buses, Zambia, bought a few RTs for service from the last batches of RTs to be withdrawn in 1978/9. More
here.
Some others went to non PSV operators for works transport etc (up to a certain point, companies' own staff transport was outside PSV / operator licensing) - Lesney (Matchbox toys) had a substantial fleet - photo on SCT61
here.
As an aside to the preserved Browns Blue RT - I understand that particular bus never ran with Browns Blue, but is a representation. Likewise, there's an RTL in Barton livery around now which also never ran for Barton.