In uk.d-i-y, maddening wrote:
We've been having power problems in our new property since we got in
although they were tolerable, namely flickering lights when something
is switched on (such as the kettle) and brief 'interference' on the TV
screen in accordance with things being switched on.

If "new" means "brand new", you need to get shirty with the developers
you bought it off. Let them know of your problem, let them have one go
at fixing it, then get a real electrician to fix it and send your
developer the bill. If by "new" you mean "place we've only recently
moved in to", the problems are all yours; lucky you...

Tonight things took a turn for the worse with the power tripping off
twice, simply because I switched on my PC! (note: the PC is fine and
further testing proved that switching on other appliances could also
trip the power - it seems that the mains simply can't take too many
things switched on at once).

Though you provide few details, it sounds rather as if you have an
earth-leakage breaker which is close to its tripping limit, such that
small extra leakages - concretely, the initial surge through mains
inlet filter networks on your PC and other domestic appliances -
cause it to trip. It's possible the ELCB itself is faulty (overly
sensitive), but likelier that you have a marginal fault in your
wiring or something connected to the ELCB side of your consumer unit,
which puts it close to tripping such that the small extra imbalance
makes it go Pop.

We're in Wales and are going to get in touch with Western Power
distribution tomorrow but I have a feeling that an electrician will be
required, hence the initial question re good, reliable electricians in
the area.

Big place, Wales. (Cue Douglas Adams mode: well, not as big as the
galaxy, but further than the chemist.) I know there's a competent
electrician in Llandogo (Wye Valley, about 4 miles upstream from Tintern),
but I can't remember his name. You'll need to be a little more specific as to
location!

Do I go for an electrician with certain credentials to avoid the
cowboys?

Personal recommendation is by far your best route: neighbours, work
colleagues, shopkeepers. Membership of trade bodies is only loosely
correlated with competence - i.e. there are incompetent rip-off
merchants who belong to trade bodies; there are good honest small
outfits who get by perfectly well on recommendation alone who don't
belong to the trade association; but a somewhat higher proportion of the
non-registered ones are less than fully up-clued.

Should we be going for an electrician first, or going through Western
Power first? (I have a feeling that the latter will say it's a problem
with our wiring and so is not their responsibility).

You're almost certainly right there - and the problem is much likelier
to be in the stuff you own than on their side.

Finally, from my description, what is likely to be the fault? Poor
wiring?

Definitely too little information for us to make a half-decent guess,
though I've speculated earlier in this reply. On sheer statistics,
you're likelier to have a fault in an appliance or something else
connected in to the circuitry, than in the fixed wiring: but either is
quite possible, and your reference to lights flickering when you
turn on a kettle does suggest a wiring problem. A merely competent
(as opposed to walks-on-water) electrician will be able to diagnose
and almost certainly fix with an hour or two's work; and since it
appears you don't have the equipment or knowledge to do the job
yourself (not an insult - I'm sure there are areas you're far more
expert in than me or an electrician!) it will be money well spent.
(As in the old story about the repair bill, itemised further at
outraged customer's request: "To: hitting piece of kit to
make it work: 50p. To: knowing where to hit it: 99.50 pounds." ;-)

Hope this helps - Stefek