Analog film photography and cameras

I've got a very loved and well-used Nikon FE that I've had since the beginning of time - its what I learned to shoot film and develop/print with at school.

The light meter seems to be a bit off, as in it constantly gives out readings that are too low. The needle doesn't seem to be stuck, it just floats at the base shutter speeds.
The battery check light is working so it doesn't seem to be power related.
Otherwise it works just fine.

Anyone know of a repair place that can look at this? I'd really like to keep it running as its such a nice thing to use.

http://www.playfordrepairs.com
http://www.qype.co.uk/place/1527440-Graham-Playford-Photographic-Engineering-London