R-R pulled out because Alan Bond's big idea was way ahead of its time and the technology needed a long programme of development with no guarantee they could make it work. So the orbiter would have been powered by conventional rockets, as Hermes/Shuttle/Buran. And as
@Archibald reminds us, the engines need to be well aft and well inboard.
The main question would then have been - vertical or horizontal launch? BAe had MUSTARD in their back pocket, so the politicians would have fought out a MUSTARD-cluster vs. Hermes-stack battle for the sake of the bragging rights, with Gorbachev's new, curtain-free Russia stepping in as a late outsider with a Mriya + horizontal mini-Buran "neither loses to the other by choosing this instead" classic gambit.
The cost vs capacity tradeoff would have also caused a battle between a manned option at unaffordable cost and an unmanned (or potentially one-manned) option of questionable usefulness. Mriya + mini-Buran would have probably needed a second-stage booster strapped to the spaceplane, but it would have split an intermediate budget across an extra payer, so might have proved politically feasible.
Was it technically feasible? Nominally, yes. But the bitter status struggles and Camel decisions that always dog international collaboration would have left it struggling to achieve orbit with a payload bigger than a postcard. The first iteration would have been a sub-orbital, unmanned spaceplane. Two semi-independent developments would have sent up a payload-incapable orbiter and a manned sub-orbital joyride.
By now the technology was obsolescent and the operational capability demonstrably next to useless. Russia was hardening off again under a resurgent right wing, costs were escalating and the will to collaborate on a refresh was fading fast. Capability was kept up to save face while the Shuttle still rode, but a planned Mriya II with ISS-rendezvous capable orbiter was cancelled.
History closed around itself and the world returned to the timeline it was always going to follow.