With my G7VZY hat on, be prepared to have to push for what you want, not all electricians, private, council or other, really  understand the subtleties of the extra requirements of a radio shack, and why you may want to do seemingly odd things like add ferrite beads  on the  mains earth if you have EMC issues.

If you are going for the TT island,  and that is a good call in this case, then 2 core SWA is fine. Gland and pirahna to connect the armour to the house earth as before but at the shack end, use an all plastic compression gland instead of a metal one,  and over sleeve the armour. You must have at least one DP RCD,  ideally in the shack but could be either end or both really.

Now,  2.5mm will certainly be OK at 25-30A but if you do need that much it will run very hot if it has to pass through insulation at either end. I'd still consider 4mm.

You may also want to include some RFI precautions such as an L-N mains filter and perhaps the option of 12V DC (non SMPS) lights as well, especially if you intend to operate on HF where things like LED lights tend to be sources of hash as do some of those USB charger sockets. Ifnot then at least leave the space for it.

I tend to design (professionally) such that all cables enter a radio room or bunker through one A3 sized metal access panel, as this ensures that the RF earth, the lightning earth and the power earth all flap together at a common point, and no expensive kit ends up doing the splits between 2 grounds.  It is not essential but it is something to thing about. A poor man's version has all the cables to the operating desk passing through a common plate and screened glanded to it.

Are you also bringing in ethernet, telephone or other ELV from the house ?

armoured cat5  is an option there if so.

Probably more I have not remembered.

Mike.

Mike, the SWA would pass through the SIP wall of the garden building so your point about insulation is relevant. No other cables as the wifi and cordless phone work well at that distance. I do operate HF and have thought about the points you raised.

Mike

Mike, the SWA would pass through the SIP wall of the garden building so your point about insulation is relevant. No other cables as the wifi and cordless phone work well at that distance. I do operate HF and have thought about the points you raised.

Mike