* FTSE 100 up 0.1 pct, mid caps hit fresh record
* UK services activity grows at fastest rate in 6 months
* TP ICAP falls after "shock" departure of finance chief (ADVISORY- Follow European and UK stock markets in real time on the Reuters Live Markets blog on Eikon, see cpurl://apps.cp./cms/?pageId=livemarkets)
MILAN/LONDON, Nov 3 (Reuters) - British shares hit a record closing high on Friday, supported by a rally in global stocks and the Bank of England's interest rate hike, which helped British exporters by putting pressure on sterling.
The exporter-heavy FTSE 100 index peaked at 7580.95 - 18 points short of June's all-time intraday record - and ended 0.1 percent higher on the day at a 7,560.35, for a 0.7 percent gain on the week.
The mid cap index also hit a new all-time high and closed up 0.4 percent on the day.
"Globally, stocks are at record highs, so it would be a pretty dire sign if the FTSE was not in on the action when the economy is just about keeping up with peers," said ETX Capital analyst Neil Wilson.
"Yesterday's sharp fall in sterling on the BoE's dovish hike was the catalyst for fresh gains as, once again, we saw a weaker pound a reason to bid up UK equities," he added.
Sterling came under renewed pressure on Friday but strengthened slightly after data showed that the services sector enjoyed a sharp pick-up in growth last month, although companies were nervous about Brexit.
The closely watched survey came a day after the Bank of England raised interest rates for the first time in a decade - by a quarter of a point - but said it expected only "very gradual" further increases as Britain prepares to leave the European Union.
Among big internationally exposed FTSE companies, Diageo was the biggest gainer, up 0.9 percent and close to its all-time high, while Experian and Compass Group added 1.6 and 0.8 percent respectively.
Domestic banks Lloyds and Royal Bank of Scotland were under pressure for a second day on the prospect that the UK tightening cycle would be very gentle.
The biggest gainer on the FTSE was NMC Health, up 4.1 percent, helped by a price target upgrade by Deutsche Bank.
IAG, the owner of British Airways, fell 1.8 percent, reversing earlier gains.
IAG said it was aiming for annual core earnings around 20 percent higher than previous targets as it stuck to its goals for earnings-per-share growth and margins for the coming years.
Among mid-caps, there were stronger price moves.
TP ICAP, the world's No. 1 interdealer broker, fell 6.4 percent after saying its finance head was leaving and flagging a challenging outlook for the final quarter of 2017.
"The shock news (on TP ICAP) is that Andrew Baddeley, CFO, is stepping down from the board with immediate effect. Underlying trading, however, is good," said Liberum, confirming its 'buy' rating.
Small-cap miner Lonmin saw a third of its market value wiped off after delaying its annual financial results, saying it could not yet give a specific figure for the impact of an ongoing business review.
It had its worst ever day on the stock market, dropping 32.4 percent.
(Reporting by Danilo Masoni and Helen Reid; Editing by Kevin Liffey)