The two boroughs have given at least one dose of the vaccine to 42.8 and 47.5 per cent of adults in this age group since jabs started being handed out in December 2020.
These figures trump the data given for the four other local authority areas in Berkshire, which all lag behind with under 40 per cent of their 55-59 population given at least one jab, according to NHS England.
However, it is Wokingham borough and West Berkshire that lead the way with the highest percentages in all other age group categories except for the under 55 population.
The two boroughs have given at least one dose to 95.37 per cent (Wokingham) and 96.14 per cent of their 80-and-over population.
On the other end of the scale, Reading borough and Slough borough have consistently given the smallest percentage of vaccines in every age group from 60-64 to 80 and older.
In the 60-64 age grouping, Slough lags 22 percentage points behind West Berkshire.
Three vaccines have been approved for use in the UK:
Each uses a two dose-system. In the UK, the second dose is being given within 12 weeks of the first.
All figures correct as of Sunday, March 14 (data published March 18).