Giles - when I tried to tax an April 1960 large winch truck as Special Vehicle (for off-road winching work) - current rate £165 - at my local DVLA office around 2002, I was advised that I could take advantage of the Historic Road Tax.
I was advised verbally that Historic Taxation would cover both work (non-load carrying, moving to / from job) and private (rallying etc).
This suggests that any pre 1973 plant and equipment can benefit from Historic taxation class. I'm sure your local DVLA office will be able to advise, although there still appears to be an element of concern about the consistency of advice (which is not surprising given the very unusual situations we in our hobby find ourselves in!).
I think the view is that if dual use the higher of the RFT rates should be paid - this would cover you for second use.
If a similar but post 1973 vehicle is used it would require tax of £165 if Special Vehicles or £165 if Private HGV, so again cost is same so usage should be acceptable to the Authorities - so long as other conditions are met....
Two points arise when using a vehicle for different purposes, which need considering carefully:
A post 1960 / pre 1973 vehicle used as 'Special Types' e.g. forklift, winch truck, etc, does not require an MOT if it is being used to move around in the course of its work. However if it is being used for private non-commercial work - e.g. taking to a rally or just out for a spin for fun - it may need a MOT or at least comply with certain C&U requirements.
The Inland Revenue have been dipping fuel tanks of vintage tractors at rallies - they say white diesel must be used if tractors is used for 'private' purposes e.g. atending a rally. This would presumably apply to any historic vehicle or special vehicle used for private purpose. So if your Beaver is to be used for work i.e. moving to or from a place of work then you should have no difficulty getting the DVLA to confirm you can use it with red diesel and taxed Historic - try your local office?. If you want to take it down the pub, or to a rally, you may need to get answers to more questions