The ONS provide a file of population estimates per local authority broken down by age and sex from 2001 to 2020 (MYEB1_detailed_population_estimates_series_UK_(2020_geog20).csv). This can be aggregated by summing over all local authorities in England and Wales.
Typically demographic data is presented as pyramids with one side showing females and the other males. In order to simplify the profile here it is presented as pooled data for both males and females. The results are in tabs so the sequence can be followed through flicking between them.
To get an estimate of the increase in the elderly population the numbers over a certain age can be compared with the numbers over that age in the previous year. Subtracting the two produces the increase.