UPDATE 2-European shares kick off 2021 with rally on Brexit and vaccine optimism

* UK banks slip after Britain exits EU's orbit

* TUI jumps as CEO expects 'largely normal' summer

* Remy Cointreau slips after Kepler downgrade (Updates prices throughout, adds comment)

By Amal S and Shreyashi Sanyal

Jan 4 (Reuters) - European shares rallied in the first trading session of the year on Monday, as a landmark Brexit trade deal and coronavirus vaccination campaigns across the continent bolstered expectations of a strong economic rebound.

The pan-regional STOXX 600 index .STOXX gained 0.7% to touch fresh February 2020 highs, with economically sensitive mining .SXPP jumping more than 3%.

Germany-listed shares in the world's biggest holiday company TUI TUIGn.DE TUIT.L rose 2.7% after its chief executive told a newspaper that he expects "a largely normal summer" this year. DAX .GDAXI was up 0.1% after a long weekend to trade below all-time highs, while France's CAC 40 .FCHI added 0.7%.

Global stocks hit record highs, with the STOXX 600 recovering about 50% from its March 2020 trough as investors pinned their hopes on coronavirus vaccines to fuel a speedy economic bounceback.

Britain began vaccinating its population with the COVID-19 shot developed by Oxford University and AstraZeneca AZN.L on Monday. distribution of the AstraZeneca-Oxford University COVID-19 vaccine is also behind the broader positive move in European stocks," said David Madden, market analyst at CMC Markets in London.

Adding to the upbeat sentiment, a survey showed German factories churned out more goods in December despite a stricter lockdown to head off a spike in coronavirus deaths. Markit's final Purchasing Managers' Index (PMI) for manufacturing rose to 58.3 from 57.8 the previous month.

London's blue-chip index .FTSE gained 1.7% in its first day of trading with Britain outside the European Union's orbit.

While the hard-fought trade deal agreed late December set rules for industries such as fishing and agriculture, it did not cover Britain's much larger finance sector, meaning automatic access to the EU's financial markets came to an end on Dec. 31. in UK banks such as Lloyds Banking Group LLOY.L , Barclays BARC.L and Natwest NWG.L fell between 0.7% and 3%, while the broader European banking index .SX7P fell 0.8%.

In a bright spot, however, Ladbrokes (LON: LCL ) owner Entain Plc ENT.L jumped 25.3% after it confirmed an $11 billion bid proposal from U.S. casino operator MGM Resorts, which it said significantly undervalued its business. betting firms like Flutter Entertainment FLTRF.L , William Hill WMH.L and 888 888.L rose between 2.6% and 3.5%.

French wine and spirits maker Remy Cointreau RCOP.PA slipped 0.2% as brokerage Kepler Cheuvreux downgraded the stock to "hold" after a U.S. decision last week to impose additional tariffs on French wines and cognac.