No transponder? No problem!
Not even required in the London CTR. Only problem there is slightly increased ATCO workload created by need to inform other agencies of the ident (eg Tower ) , plus 'goody-goody' phone calls from other agencies worried that it might be an intruder. Fair enough.
FIS without a transponder? Well, we all know by now, don't we

, that FIS is a non-radar service anyway, so no problem.
If in doubt about any particular airspace look in the UK AIP to establish carriage of SSR requirements.
Downside is no conspicuity and slightly less protection because you would be blind to TCAS and STCA so be vigilant with the look-out, not that you wouldn't be of course! And don't get lost or in trouble because you will be harder to find. And if one is naughty one is harder to track and trace.......
Mr Cross says: "A number of times I have come across zones where they have primary radar switched off".......Where's this happening then ? Most radars in the UK these days are 'Combined Plot Extracted' or primary with SSR overlay. Unusual to have Secondary only displayed if the Primary is servicable because separation standards have to be increased with SSR only.
TDM