We moved into a new place last December and our surveyor warned us to get an
electrical inspection done.

The outcome of the report showed a number of areas that needed attention,
but one thing that did not come up on the report is that if any high power
device is switched on (e.g. electric shower, drill, oven, etc.) the lights
dim slightly. The dimming is not huge, but definitely noticeable.

I've done a quick survey of each of the MCB's off the consumer unit and
confirmed that the lights (with one exception) run off dedicated fuses.

Am I right to worry about this, and if so, can anyone suggest what is
happenning?

Cheers,
Chris