For example, Google quotes the price of IAG on 31 Jan (before rights issue) as 229p, but Stockopedia shows it to be 337p. Google adjusts pre-rights issue prices by dividing the market cap at that time by the new number of shares outstanding after rights issue. This essentially gives the value of your shares if you do nothing at the rights issue and let it dilute your shares. So on 31 Jan the price of IAG would have been around 572p (the rights issue was 3-for-2). If you purchased shares on 31 Jan and fully exercised your rights to the new shares at 92p per share, then your average cost would have been 284p per share. So I have no idea how the 337p shown in Stockopedia's chart (which in fact matches the data shown on Financial Times' chart) is calculated.
It's not a situation a have been following, but there are a couple of things I can observe.
The closing share price on 31st Jan measure contemporaneously was 569.2p - close to what you have quoted.
From the RNS following the fundraise
We can deduce
Original Shares : 2,207,952,543
New Shares : 2,763,523,467
Total resultant Shares : 4,971,476,010
So it wasn't precisely 3 for 2. I think the way they did the scale-back left some potential new shares un-issued. The ratio was actually 1.45
That would suggest the Google restated price (on the methodology you quote) should have been 232 rather than 229 - but that's pretty close. (There might have been something else small between Jan & October that Google adjusted for ?)
AHA
I should have thought to look at this before I did the calcs above (and concluded that I could not understand the Stocko Historical number.)
If you compare the Google & Stocko price quotes for 1st October (before the new shares were born) they both show 93.82p (as does Yahoo) so it looks as though, whatever the anomaly is, it relates to something else that happened earlier in the year and not the recent rights issue.
I don't know what that might be.
If you wanted to sleuth precisely when the anomaly occurred and therefore what the cause might be, as far as I can see Yahoo (unusually) have not adjusted the historical prices (yet?) so you can see the contemporaneous prices here you can tell as the 31st Jan price shows as 569.2.
If Murphy's Law applies and Yahoo update the price history before you read this - I have just downloaded their price history as of now, so will happily share it if that is the case.
I am sucker for anomalies like this, so oftentimes I would do the sleuthing, but I'm a little time poor ATM.