We have used Allied Pickfords from UK to AUstralia and Australia to CH.

They do not tend to break stuff, and they always had the cheapest quotes for us, but on arriving in SWitzerland they showed up a day later than they said, without warning. If you can live with that, they are ok otherwise.

Someone once told me to always get the insurance with an independent company as the same company will tend to rip you off once you need them.

Count on storage being expensive, as you tend to have to use it longer than planned. IF only for a few months, it might be ok, but I do not know about UK prices.