The FTSE 100 was up 0.3%, while the FTSE 250 rose 0.5%, with builder Galliford Try leading gains after announcing job cuts.
After weeks of waiting for significant updates on Brexit, investors welcomed a "new deal" for Britain's departure from the European Union set out by Prime Minister Theresa May, which offered the prospect of a possible second referendum on the agreement.
That thrust housebuilders 1.2% higher, their biggest one-day rise in a month. Persimmon and Taylor Wimpey were among top gainers on the main index.
Heavyweights HSBC, Prudential and Standard Chartered also offered support as markets hoped that trade tensions between Washington and Beijing would ease after the United States eased restrictions on telecom giant Huawei.
"While it's a small measure, it does perhaps symbolise that there might be a reverse gear from the current slide to what could well turn into a full-blown trade war," CMC Markets analyst Michael Hewson said.
Shares of Lloyds and Barclays gained as Tesco's decision to stop mortgage lending raised the prospect of reduced pressure on margins, due to lesser competition.
Keeping a lid on gains were exporter stocks that weakened as sterling strengthened after May's latest proposals.
On the FTSE 250, Galliford Try jumped 15.3% on its best day in over a decade after the company said it would cut up to 350 jobs as its construction business focuses on its core strengths, bringing hopes of improved margins.
Galliford's update "should be taken well because there are no further incremental contract issues, and because part of the exceptional cost identified in April has a payback through future cost reduction," Liberum analysts said.
Britain's largest industrial distribution firm Electrocomponents rose 7.8% to a seven-month high after reporting profit ahead of market expectations.
UDG Healthcare scaled a more than eight-month high with a 6.8% rise, after the company raised its 2019 adjusted profit forecast.
Metro Bank, which has seen its shares hammered after disclosing an accounting error, advanced 7.5%. The lender's annual meeting results showed it had escaped a threatened major investor challenge on Tuesday, though there were sizeable votes against several of its top directors.
Keeping a lid on gains among midcaps was Entertainment One, the maker of children's TV show Peppa Pig, that slumped 11% after missing estimates for revenue as well as Royal Mail, which slipped 9.2% ahead of earnings report.
(Reporting by Shashwat Awasthi in Bengaluru; Editing by Keith Weir and Gareth Jones)
By Muvija M and Shashwat Awasthi