Indoor Grape Vine

It looks as if they have not been pollinated, the fact is they have not made any seed only fruit , like you can buy seedless Grapes.. You may have to pretend you are a Bee and make sure the pollen is transferred to the stigmas. Or obtain a flowering branch of another Grape Vine to ensure cross fertilization, as it may be like Apples needing a mate.

It may be your culture method, now is the time to prune, hard back to the main rods, bring the rods down to a horizontal level.
Feed the root area with blood, fish and bone, super phosphate and sulphate of potash, plus a good mulch of humus.
In February thin out the developing buds, tie the rods back up to main support.
Stop growth at 2 leaves after developing bunches of grapes and tie in, then one leaf on side growth.
Watch out for adult vine weevil in May.
Thin out bunches in July.

Just a little addition,
When we pollinated we cut down on spraying and damping down, letting the flower open.
Bang the main rods about midday for three or four days.

maybe your not watering any wear near enough

My recollection is that grapes are wind pollinated not insect pollinated. I may be wrong, but cross-pollination is always preferred. I would suggest Siegerrebe, and all the Angevines and possibly Muscat of Norwary. Doctorbob is correct in his suggestions.

This is a long issue, and I would suggest a web search for British viticulture links.

I put in a vineyard with low heat index grapes. Madeline Angevine, sylvaner, Muscat, Mueler Thurgau and two red grapes. Dornfelder and Dunkelfeder. Regen might have been a better choice. I am propagating the latter.
If you planted a Merlot, or Pinot or other high heat index grape, nothing you do will help.

First horizontal arms are at 1 ft. above the ground, and I keep them to only four feet in each direction. Three upgright spurs. Fruit, thinned to three clumps ea. I also have two replacement canes to replace last years horizontal arms.

In a greenhouse training and everything would be different.
Is the greenhouse glass or fiberglass? If the latter you may simply not be getting enough light. Such materials deterorate after a time.

This is one home grown fruit that I generally say. BUY IT.
Same for the vineyard I started. The yield vs. the expense and labor just is not profitable. Even most wineries that are successful, are not because of sales of their wines but of the gift store add ons. This is one hard way to earn a living.

I explained the culture methods for dealing with grapes for personal use, we are not talking mass production. They are being grown on a small scale for personal use.
Adult vine weevils are active in May and will feed on the tender parts of the vine, hence damaging the grapes in their infancy.
Our method of control was to place young Hydrangea leaves on the floor of the vinery and inspected them and caught and destroyed the adults, replacing the leaves as they withered until the insects had been destroyed.

Doctorbob, That is a great idea. We may have a different vine weevel here. So far I have seen no activity on the grapes or hydrangeas. Strawberry Vine Weevil, is what we have. It works on Rohodendrens and Bergenia and is devastating on strawberries..

Bergenia leaves would be my trap leaf here.
Here in the Northwest, bee activity is nill at the time the grapes blossem If insects are involved it would be bumblebees or mason bees. I do not have mason bee nests up there, so I do think some are self-fertile, and those that are not are benifited by having other varieties planted near by.

I suspect that mason bees would be benificial, but not necessary. In a greenhouse, bee presence would be necessary, as well as having two or more different plants.