interference with FM: wi-fi or bluetooth?

The FM hiss is not coming from the RF sections of the unspecified wi-fi or BlueGoof device. It's coming either from the digital logic associated with the unspecified device, or from the switching power supply associated with the unspecified device. Unplug the power the unspecified device to see which one is the source of the hiss.

I would guess(tm) that the noise is arriving via the AC power line and not being radiated through the air. Try plugging the FM radio into a different wall outlet from your unspecified device that is allegedly making the hiss. It's also highly likely that your FM radio is equally at fault. The FM radio should be able to reject power line noise. Reading between the lines, my guess is that you hear the hiss on any FM channel, which suggest low frequency conducted noise, and not higher frequency RF noise.

You didn't supply sufficient information to properly determine the source, so I suggest you do this by replacement. Find another FM radio and see if it has the same problem. If not, your most likely culprit is the FM receiver. Also try another brand or model unidentified wi-fi or BT device. If that also exhibits the same problem, then your problem is still the FM receiver.

If the severity of the problem is minor, you might try relocating the two interfering devices away from each other. Also, power line EMI suppression ferrite beads can help if it's low frequency switching noise.

Good luck.

Does it also lack the hiss when run off batteries even when mains is on?

A better solution might be a fixed yagi antenna or dipole up high to give the receiver a much better signal to start with. That was my solution to getting optimum results with my FM tuner on stereo.

DAB is another kettle of fish altogether and either works or fails dismally. UK DAB implementation is dire :(

I can't see 2.4GHz or 5GHz WiFi encoding causing any detectable signal at FM frequencies. It is more likely a noisy switched mode PSU or a PC with a badly earthed case or stupid transparent plastic sides.

Neither. Cheap switch mode PSUs with poor or no suppression which could come with just about any random product you buy these days. A ferrite choke on the power lead(s) might help cut down on it.

A process of trial and error to find the offending kit might well be worthwhile. Chances are there is one major local interference source.

ADSL can interfere with AM broadcast frequencies and vice versa. Where I live the SNR changes radically after sunset as distant high power European AM radio stations bounce back down onto the UK.

My battery powered radio will be tested at various distances from the blue tooth keyboard and the tiny computer stuck on the back of the monitor. The answers so far are reasonable and some experiments will be reported tomorrow.