The UK travel and leisure index declined as much as 1.5%. It later pared losses to trade 0.5% lower after BioNTech and Pfizer said a three-shot course of their vaccine was able to neutralise the Omicron variant.
Airlines Easyjet, Wizz Air and British Airways owner IAG, and public transport companies FirstGroup, Stagecoach and National Express dropped between 2.5% and 4%.
Leisure stocks such as cinema chain operator Cineworld, pubs Wetherspoon and Mitchells & Butlers, and Restaurant Group slid 2%-5%.
The tougher rules could include advice to work from home as well as COVID-19 passports for large venues, the reports said.
A spokesperson for British Prime Minister Boris Johnson's office had no immediate comment on the reports.
(Reporting by Yadarisa Shabong in Bengaluru; editing by Uttaresh.V)