The number of recorded live births in 1935 is 711,426. This is broken down -
England 559,569
Wales 39,187
Scotland 87,928
NI 24,742
Deeper figures by sex and date appear only to be available from third party data organisations by subscription. Excel spreadsheets are available in many areas of ONS, but just to warn they are not always safe to open. Just take care.
The 6 May 1935 was a Monday. Based on more recent data, which may not be correct for 1935, 14% of births occur on a Monday. That would extrapolate to 99,600 births occurred on average on the 52 Mondays in 1935, or 1,915 for each of those Mondays.
Average monthly births for May were 56,071 over the period 1995-2014, again this may not be representative but it is a start. It also represents 8.49% of annual births. If we assume an even spread over the month that would be 1,808 for each Monday in May.
Therefore 711,426 x 14% x 8.49% x 25% (four May Mondays) gives a very crude figure of 2,114 extrapolated back to 6 May 1935.
An even cruder reconciliation is to divide 711,426 by 365 days = 1,950 daily average ignoring other trends above.
Without 'squaring up' and working out the standard deviation from the mean and stuff (which goes over my head these days) let's just say :
(1,915 + 1,808 + 2,114) divided by 3 =
1,946 probable numbers of live births on 6 May 1935.
So long as other grandmother's were not, like your grandmother, holding it all in to celebrate the Silver Jubilee of King George V which also took place on that day.