It's very strange, I've been a Doctor Who fan since I was a kid but didn't really look into a lot of classic british scifi.
I think it was finally giving Blake's 7 a try that spurred me on.
Until I watched it I thought Sapphire and Steel was a romance series.
I've now worked my way through Survivors, Doomwatch, Omega Factor (which is awesome), Moonbase 3 and went back further to shows like Timeslip.
If you have any more suggestions of similar shows please let me know.
I recently finished up with DOCTOR WHO, as of the 2017 Christmas special. Any further viewing will be restricted to AN UNEARTHLY CHILD through to THE TIME OF THE DOCTOR. However, I doubt I'll venture much beyond DOCTOR WHO with Paul McGann.
I've always been a huge fan of SURVIVORS, BLAKE'S 7, UFO, DOOMWATCH, MOONBASE 3 and so on and so forth.
For further viewing, please consider...
RED DWARF.
SPACE 1999.
THE DAY OF THE TRIFFIDS (1981) - 6 part TV series. 3 hours total. Avoid
all other versions.
THE HITCH-HIKERS GUIDE TO THE GALAXY (1981) - 6 part TV series. 3 hours total.
Anything to do with Professor Bernard Quatermass, especially the TV series from the 1950s - or what's left of them.
Also plenty of black and white British sci-fi films available on YouTube. In fact, most of the sci-fi from the 1940s, 1950s and 1960s on YT is fairly enjoyable.