UPDATE 2-Brexit optimism breathes life into UK-focussed stocks

* FTSE 100 up 0.3%, FTSE 250 up 1.2%

* LSE gains after rejecting Hong Kong bid

* Homebuilders biggest gainers on both indexes

* Brexit-sensitive stocks jump

* Dollar earners weigh on main index (Adds news items, analyst comment, updates to closing price)

By Yadarisa Shabong and Muvija M

Sept 13 (Reuters) - UK stocks ended Friday on a high note as optimism that a no-deal Brexit could be avoided spurred a rally in stocks with domestic exposure, overpowering losses in blue-chip exporter stocks that were hit by a stronger sterling.

The FTSE 100 rose 0.3%, with homebuilder Barratt jumping nearly 6% to top the gainers. The country's big banks Lloyds, Royal Bank of Scotland and Barclays added more than 5%.

The mid-cap index climbed 1.2% to a near one-year high, tracking gains in the local currency.

A surge in the pound was triggered by a media report that Northern Ireland's largest political party had agreed to accept some European Union rules after Brexit.

Adding to the positive sentiment, British Prime Minister Boris Johnson said there was "the rough shape of a deal to be done" over Brexit, as he prepared to meet European Commission President Jean-Claude Juncker next week in a renewed push to reach an agreement.

"Sterling's breakout coincides with a breakout of optimism, albeit slight, that a thaw in the impasse between Brussels and London may be beginning," City Index analyst Ken Odeluga said.

Gains for the pound prompted a sell-off in exporter stocks including Diageo and British American Tobacco, keeping a lid on FTSE 100's gains for the day.

An index of housebuilders, which are vulnerable to a hit to house prices in event of a disruptive no-dealcBrexit, rose 0.7% to its highest since late July.

London Stock Exchange gained 3.6% after it rejected a $39 billion takeover offer from Hong Kong Exchanges and Clearing . The Asian bourse responded by saying it would continue engaging with LSE shareholders regarding the bid.

The FTSE 100 took home its third straight week of gains as hopes for more stimulus and signs of improvement in global trade relations have helped the index recover after suffering its biggest monthly fall this year in August.

Adding fuel to the rally, Credit Suisse turned bullish on UK stocks, especially those with international exposure, as the chances of the country crashing out of the European Union fall and some equities look cheap compared with foreign counterparts.

Broadcaster ITV rose 5% after Liberum called SDN, its digital multiplex operator, a "hidden gem" that could fetch up to 750 million pounds to 1 billion pounds if sold.

While housebuilders were powering gains for the midcap index, gold miner Centamin plunged 7% after downbeat production forecast. (Reporting by Yadarisa Shabong and Muvija M in Bengaluru; editing by Arun Koyyur and Toby Chopra)