Blue chip shares closed up as sterling fell after dovish comments on interest rates from Bank of England governor Mark Carney.
The Bank said it expects inflation to hit its intended 2% target in the current quarter, before climbing as high as 2.7% in early 2018, as a weak pound makes imports more expensive.
The FTSE 100 Index lifted 48.7 points to 7156.3, after Carney said rates could move in "either direction", which for many traders lessened the prospects of rate rise later this year. The FTSE 250 Index rose 19.3 points to 18259.5.
The pound fell by almost 1% against the dollar to 1.2543.
Top flight shares appeal to investors when the pound falls because most of the sales of firms in the index are earned aboard, boosting revenues when translated back into sterling.
The Bank also expects the economy to grow 2% in 2017, up from a November forecast of 1.4%, which was itself an upgrade from the 0.8% forecast made in August. It kept interest rates on hold at 0.25%, as expected.
In the top flight, Royal Dutch Shell said profits last year were held back by the cost of its £50bn ($62.7bn) purchase of BG Group, and a lacklustre performance from its oil and gas trading arm.
Shell, the UK's biggest oil company, saw 2016 profits fall from $3.8bn to $3.5bn. However, the group maintained its total dividend for the full year unchanged at 1.88 cents per share. Shares jumped 35p to 2255p.
The biggest risers in the FTSE 100 Index were Smurfit Kappa (+94p to 2162p), Reckitt Benckiser (+279p to 7109p), Randgold Resources (+200p to 6815p), Compass Group (+42p to 1439p) and Paddy Power Betfair (+205p to 8535p).
The biggest fallers in the FTSE 100 Index were Worldpay Group (-7.6p to 280.1p), Capita (-12.1p to 487p), 3i Group (-15.5p to 692.5p), Johnson Matthey (-42p to 3240p) and Legal & General (-2.8p to 232.8p).
The biggest risers in the FTSE 250 Index were GVC Holdings (+39p to 655p), Centamin (+7.1p to 167.4p), Acacia Mining (+15.8p to 436.1p), Kaz Minerals (+17.5p to 505.5p) and Rightmove (+123p to 4162p).
The biggest fallers in the FTSE 250 Index were Mitchells & Butlers (-13p to 258.4p), TalkTalk Telecom (-6.2p to 162.2p), Wizz Air (-56p to 1560p), Nostrum Oil & Gas (-16p to 460p) and Petra Diamonds (-5p to 147.8p).