This seems to be quite a common problem with the 6910. Gumtree and Ebay frequently have secondhand Sunbeams advertised with comments to the effect that the machine works well but the pressure gauge does not give a reading.
Recently I have repaired two machines with these symptoms and in both cases the problem was caused by a blockage in the same place - the vent hole in the brew head thermoblock which leads to the pressure gauge "T" and the solenoid valve.

A close examination of the blockage site has revealed what is most likely the cause of the problem - a very narrow section at the internal bend where the drilled gallery meets the metal tube leading to the pressure gauge and solenoid valve. In a poorly maintained machine this point blocks solidly with oils and grounds and is very difficult to clear because it is so narrow.
Because of the small size of the opening it is often difficult to get a piece of wire into it to clear it or it can take a lot of pressure and soaking with cleaner to blow it free, as well as the need to dis-assemble much of the machine.

I have found that perseverance with a thin piece of stiff wire in this drilled hole can usually open it enough to get the cleaning solution moving through it without resorting to a major tear-down but it does take quite a bit of pushing and jiggling.

It appears that this restriction is caused by a manufacturing flaw and I have been tempted to try carefully drilling it out but, without knowing how close it is to the internal heating element and spiral water tube, have thought better of it. If anyone has an old 'burnt out' thermoblock it would be helpful if they could carry out a post mortem on it with a hacksaw in this area to see if drilling would be a safe option as it would certainly keep a lot of these machines operating more reliably and out of landfill.

I have attached some photos to help illustrate what I have been describing - one shows the plumbing in the thermoblock (please excuse the hi-tech labels but I was in a hurry) and the other is taken down the drilled hole with a light source shining in the side tube to show the very narrow opening.

down the hole.jpg