I think to do a Sidestep-Visual at LHR in that situation you may as well go-around.
You can have it like this if i am correct.
27R I-AA BAW98PL 2 miles to go. KLM883 7 miles to go. UAL921 11 miles to go.
27L I-BB AAL133 4.5 miles to go.
Seems practical.
Regards,