Just as an update, I took the boat down to the solent yesterday, and had a great time. The only downside was the continuing problem with the trim / tilt. It was a little embarrassing at Priory Bay when I could not tilt the engine for about 5 mins when coming in. I have had another look today, and cannot fathom it at all. It will tilt fine for about three quarters of one full down or up movement. Then it slows and slows and then finally stops. Then it is dead for about 5 mins, when it will work again for another movement, and so on.
During the dead period, the engine will turn over on the starter, so I think the main wiring to / from the battery is fine, as I am sure the starter takes more power than the trim / tilt.
The relays seem to click, and so I suspect there is something wrong with the trim motor. When I put my hand on it, it is quite warm to the touch. is this normal? Could it be that heat causes the case to expand, and this takes the brushes out of contact, or something similar?