There were also 31,214 remortgage approvals in the month, also up from 29,713 in March.
Gross mortgage lending was £11.5bn in the month, compared to the previous six-month average of £12.4bn, while repayments in April were £11.3bn, compared to the previous six-month average of £11.5bn.
Samuel Tombs, UK economist at Capital Economics, says on balance, April’s lending figures paint a fairly weak picture.
He says: “Granted, the number of mortgages approved for new house purchase rose from 51,100 to 51,800, despite the fact that the Stamp Duty holiday for first-time buyers ended at the end of March.
“Nonetheless, the level of approvals is still some 3% below its level at the end of last year, and surveys suggest that new buyer interest is increasing at a fairly sluggish pace.”