if you are only getting 'briar' roses off the root stock, then the graft of the cultivar rose has died. the root stock is probably the stronger of the roses.

hard pruning is not going to encourage the original bloom. sorry.

Seaburngirl is right - check the plants carefully to see if there's any part still producing the original flowers. If there is, then you need to remove all the other sucker branches and stems at their point of origin, below the graft.

Thank you both for your answers. I’ll go and look for signs of the original bloom in the morning. How disappointing!
Thank you anyway.

This is an issue that goes back to the hybridizer. It's not your fault. He/she selected a cultivar with inferior chromosomes in favor of more marketable attributes - color, fragrance, size & physical appearance, etc. Hybrid roses require maintenance. Sometimes nature wins.

That's not strictly true; Rosa rugosa rootstock is vigorous, that's why they graft many varieties of roses onto it, to give the grafted part vigour, but it also means that an eye should be kept out for sucker growth off the rootstock. This should be removed as soon as it appears to prevent it taking over the plant - if its not noticed, over time, it does take over, stealing nutrients from the grafted parts, which then dies.

I just meant when it comes to species vs hybrids, the species typically wins out because it tends to be more vigorous & overtakes the grafted on hybrid. Those suckers from the rootstock must be kept in check or it will take over. That's what I meant by 'require maintenance' in my previous post.

Yeah, you do have to be vigilant with Roses. I am for ever removing shoots from the base of my standards. One year I failed to notice one right at the base of the graft and it flowered. The flowers were actually beautiful, but I wanted to keep my standard. I removed the 'offending' shoot and it has been fine since even though it was a really big shoot and meant I lost about a third of the top growth. Now I am more vigilant, but I often think of that 'rogue' branch and sigh ...it was ever so lovely. Double pink flowers of a floribunda kind. No idea what rootstock that is.

Before you dig up your healthy root stack and bin it why not take the opportunity to graft on a new rose. There are plenty of sites willing to show you how see this one https://www.wikihow.com/Graft-Roses.