I think you're defining East and West in weird ways in order for this to make sense. Maybe it's because Hyde Park shifts the real "centre" of London off to the left (e.g. Charing Cross is 'sort of' the middle but isn't really.)
If you compare like for like it's much closer. e.g. go 3 miles east and 3 miles west from a 'centre' and compare prices. There's not a 70% difference unless you end up in an outlier (e.g. South Ken).
Last year a 2 bed in Hammersmith was ~1500. I think that would compare fairly well with the other side which would be near Canary Wharf somewhere.
If council tax were unfrozen and allowed to go up this effect would be mitigated and rents might actually go down.
So yes, less than 4%. A lot less.
>>> (925/650.0) (1.0/20)
1.0177975914387338
Note that 20 years of +1.78% per year does +42% compounded.
>>> 1.0178 20 1.4231442772353857
In real money, the rent for your place has gone down, not up, ignoring the furnishing.
(925/650.0) raised to the power (1/20) is 1.0178
1.0178 raised to the power 20 is 1.42
I moved into a flat in 2003 and moved out of it in 2011. The rent barely changed the whole time (~1350/month to ~1450). I've seen the exact same flat for a similar amount. Marylebone.
I bought in 2000 and sold in 2015 for three times what I paid. The main people buying where I lived in East London, were from West London where rents were so high it was effectively cheaper long term to buy in East London. Number 47 on this page. https://www.rightmove.co.uk/house-prices/E10-6QB.html
My son-in-law and his wife had moved back in with us a year or two earlier because rents in East London had gone up. In 2015 a typical 2 bed flat in East London was £1,400 per month, West London around £2,500.
There's a simple reason why house prices and rentals in London have gone up. Demand due to mass migration. Back in 2015 London's population was at an all time high, numbers not since seen 1939 apparently. https://www.trustforlondon.org.uk/data/londons-population-ov... Many properties were bought-to-rent though that got hit by changes in law.