Although the London Stock Exchange is an exchange we don't cover in our services, when we were researching this exchange for coverage viability several years back we observed some interesting points that are relevant to this question. At that time, we purchased/subscribed to several vendors' data.
Multiple platforms on one exchange
The separate trading platforms used by the London Stock Exchange each had different price reporting. For example, the electronic order book-based platforms reported actual trades in the daily OHLC summaries but the market-maker-based platforms were reporting midpoint of the bid/ask. Where a stock traded on multiple platforms there were significant discrepancies in the OHLC.
The following comments relate to data discrepancies in general:
It is important that you know exactly what the open, high, low, close and volume represent. i.e. which trades (or quotes) are used, what time periods are used and which condition code(s) are excluded/incorporated. - e.g. consider the effect of block trades, multi-leg trades, cancelled/busted trades etc.
With cross-border/cross-exchange trading also available for some securities, if you are looking at consolidated/combined trading feeds, you need to determine which rules are in place for such trades too.
Historical data adjustments
Historical data can be adjusted for various corporate events such as stock splits, spin-offs (de-mergers), stock dividends, special dividends, special distributions, capital distributions, normal dividends, distributions in a currency other than the trading currency, events that give the holder a choice of multiple options etc. There are often different interpretations for the surviving entity of spin-offs/de-mergers too.
Lastly, it may just be data error(s) made by the data supplier (e.g. corporate actions that have subsequently been changed/cancelled)
Discrepancies are commonplace. Ask your provider how they handle all of the above if it is not documented.