The pan-European STOXX <.STOXX> index was up 0.1 percent, having fallen as much as 0.7 percent just before May began speaking. Britain's blue-chip FTSE <.FTSE> fell 1 percent to the day's low as the sterling surged on May's speech.
Concerns over a hard Brexit had weighed strongly on the pound helping the FTSE end at record highs earlier this week.
May said Britain would leave the EU's single market when it exits the EU but promised a parliamentary vote on any deal and stressed it would seek to stay a key European partner.
"Markets and sterling moved higher after May said the final decision is going to be taken by parliament. That could let (investors) assume that hard Brexit may be slightly more soft," said Carlo Alberto De Casa, Chief Market Analyst at Activtrades.
Europe's banking index <.SX7P> rose 0.8 percent, reversing earlier losses and making it the biggest sectoral gainer in Europe. Top gainers were UK's Standard Chartered (>> Standard Chartered PLC) and Royal Bank of Scotland (>> Royal Bank of Scotland Group plc), both up more than 4 percent.
"Banking stocks are also performing (well) after May's declarations relieved fears of an exodus of UK-based banks, said Yann Quelenn, market analyst at Swissquote Bank.
"Single market access is key and abandoning would spell the end for such institutions to provide services across the EU," he said.
Italian banks <.FTIT8300> rose 1.8 percent, helped by an upbeat note from Goldman Sachs.
"Since the Italian referendum, market repair has accelerated: while the stock of non-performing loans at banks is likely to take time to revert to average levels, a series of announcements by banks should be positive steps towards market repair," Goldman said in a note.
Travel stocks <.SXTP> were also in demand, with the sectoral index up 0.7 percent.
Lufthansa (>> Deutsche Lufthansa AG) rose 6 percent, attracting interest after an Italian paper reported Abu Dhabi-based Etihad was interested in taking a stake in it, while Easyjet (>> easyJet plc) and Ryanair (>> Ryanair Holdings plc) rose 3.7 and 0.8 percent respectively.
May said that maintaining the common travel area with Ireland will be a priority.
Basic resources stocks <.SXPP> remained weak, down 0.4 percent, hurt by lower prices. Anglo American (>> Anglo American plc) and BHP Billiton (>> BHP Billiton plc) both fell more than 2 percent.
Shares in German fashion retailer Zalando (>> Zalando SE) were the biggest STOXX faller, down 6.7 percent after its sales growth disappointed expectations.
(Additional reporting by Helen Reid; Editing by Hugh Lawson)
By Danilo Masoni