* FTSE 100 up 2 pct
* FTSE 250 up 1.2 pct at 1-1/2 month high
* Banks, industrials lead gains on the main index
* Sophos tanks on mid-cap index after trading update (Adds milestones, updates to closing prices)
By Muvija M and Shashwat Awasthi
Jan 18 (Reuters) - British blue-chip stocks rebounded sharply on Friday to bag four weeks of gains despite a tumultuous week in UK politics, helped by improving global sentiment prompted partly by signs of easing trade tensions between the United States and China.
The FTSE 100 advanced 2 percent after trading lower most of the week as sterling rose amid tumultuous updates in UK politics and the mid-caps were up 1.2 percent at their highest in a month and a half.
Both indexes finished the week in the black to mark their fourth week of consecutive gains, undeterred by a massive defeat of the Brexit draft deal in parliament and an unsuccessful no-confidence vote against Prime Minister Theresa May.
A Bloomberg report that China has offered to ramp up U.S. imports accelerated the rise in global stocks that was sparked by another report that said Washington was considering lifting some or all of the tariffs imposed on Chinese imports.
Financial services led the gains on FTSE 100, recovering from a sell-off on Thursday caused by a profit warning from Societe Generale. HSBC rose 2 percent.
Oil majors BP and Shell also provided support as crude prices rose after data showed OPEC output fell. Easing trade frictions also contributed to the rise.
Reuters reported that U.S. President Donald Trump is reviving efforts to win approval for a significant infrastructure plan.
British industrial stocks swiftly climbed to their highest since November. Equipment rental company Ashtead was the biggest gainer on FTSE 100 with a 4.5 percent rise.
However, the prospects for Brexit remain unclear at the end of a chaotic week.
May and opposition Labour leader Jeremy Corbyn deadlocked over how to leave the European Union, while veteran Brexit campaigner Nigel Farage said the UK was likely to delay its departure and that another referendum was possible.
“Whilst (the UK’s) political conditions are dreadful, at least a hard Brexit looks largely off the agenda and parliament could even force the government to essentially abandon Brexit altogether,” City Index’s analyst Ken Odeluga said.
Housebuilders, some of the stocks most affected by Brexit outcomes, rose 2.4 percent in their best day in nearly six months.
Corporate news drove some moves initially but stocks gave in to the overall cheery mood.
Shares in Ryanair, Europe’s largest low-cost carrier, recouped the day’s losses to close 0.9 percent higher after initially falling to their lowest in nearly four years on its second profit warning in three months.
Among a handful of losers, mid-cap security software company Sophos plunged 17.6 percent after flagging lower annual billings.
Reporting by Muvija M and Shashwat Awasthi in Bengaluru; editing by Gareth Jones