It is mapped correctly as is, you can see that routing software behaves correctly here: https://www.openstreetmap.org/directions?engine=fossgis_valhalla_car&route=53.381053%2C-1.480869%3B53.381533%2C-1.481336

I have straightened the Regent Street side to match the road layout.

Sadly this isn't an issue with the data, but the road layout. I cycle this route myself and have seen the issues that it causes.