LONDON, Jan 6 (Reuters) - Sterling hit its highest in nearly four months against both the dollar and euro on Tuesday, buoyed by improved global investor sentiment, easing worries about Britain's fiscal position and hints of Britain pursuing a closer relationship with Europe.

The pound hit its highest since mid-September on the dollar, and was last flat on the day at $1.3536, while the euro dropped as low as 86.44 pence again, its lowest in nearly four months, extending the previous day's 0.57% fall.

The move in euro/sterling was particularly notable as British and euro zone interest rates have largely moved in unison - relative changes in interest rates are often major factors in currency moves.

Instead, analysts pointed to a melange of factors behind sterling's strength.

Lee Hardman, senior currency analyst at MUFG, noted the pound typically outperforms when investor sentiment is positive - world stocks are at record highs - and that as the pound had now recovered all its losses in the run-up to last year's budget, it seemed to be benefiting "from the reduction in UK fiscal and political risks in the near-term."

British finance minister Rachel Reeves, in November, raised taxes to a post-war high, giving her greater room to meet her deficit-reduction targets.

On top of that, currency volatility is fairly low, making carry trades attractive - these see investors borrow in low-yielding currencies to buy higher-yielding ones, and British rates remain higher than many peers.

As well, Hardman said, "the stronger pound could have been encouraged by recent comments from government officials indicating a desire to return to a closer trading relationship with the EU."

Britain should seek closer alignment with the European single market on an "issue-by-issue" basis when it is in the national interest, Prime Minister Keir Starmer said on Sunday.

Also in the mix, but having little effect on the pound, was data showing Britain's dominant services sector ended 2025 on a weaker footing than previously thought.

(Reporting by Alun JohnEditing by Ros Russell)