* Sterling recovers after worst day since week after Brexit
* Signs of political instability raise fears of more weakness
LONDON, Nov 6 (Reuters) - Sterling recouped some losses on Monday after slipping against the dollar for three consecutive weeks, but any strong gains were checked by continued uncertainty around Brexit talks and instability in the governing Conservative party.
Investors are monitoring the negotiations around Britain's future relationship with the European Union for the impact not only on business confidence and economic growth, but also on the likelihood of further interest rate increases, after the Bank of England's decision to raise rates last week.
BoE Governor Mark Carney said on Thursday that the bank plans two further rate increases in the next three years, but that the outcome of Brexit talks remains a factor shaping future interest rate policy.
"All of the BoE assumptions right now are based on a smooth, transitional Brexit," said Craig Erlam, market analyst at foreign exchange trading firm OANDA. "So should we run into any difficulties, that would be negative for the pound, because it would suggest those two rate hikes may not materialize."
Sterling was up 0.3 percent against the dollar on Monday at $1.3120, after falling for three straight weeks.
Against the euro, it was up half a percent at 88.30 pence. .
Britain's most powerful business lobby group urged British Prime Minister Theresa May on Monday to provide clarity on how Brexit will work, but she responded with few details beyond reiterating plans to seek a transition deal as soon as possible .
The group, the Confederation of British Industry, said on Sunday that almost two in three British companies will have contingency plans in place by March for the possibility that Britain leaves the EU without a deal.
Britain enter the next round of Brexit negotiations at the end of this week, during which the all-important topic of its future trade relationship with the EU is due to be discussed for the first time.
But it enters the process in a climate of instability, as Westminster struggles with a sexual-harassment scandal that has led to high-profile resignations, which threaten May's already slim majority.
"Once again, the UK's House of Commons seems to be shaken by personal misconduct allegations affecting both main parties," said Hans Redeker, global head of currency strategy at Morgan Stanley, in a note to clients on Monday.
Should certain ministers be forced to resign, the balance between supporters and opponents of Brexit could be upended, he said.
(Reporting by Polina Ivanova; Editing by Saikat Chatterjee, Larry King)