Those figures do seem too high. Perhaps it was an over liberal interpretation of what constituted a burn mark on the Campbell Stokes sunshine recorder card.
I remember reading many years ago of the competition for the highest sunshine totals between different seaside resorts and how this resulted in some observers measuring the faintest scorch mark on the sunshine card and including it in the total.
Buxton recorded 1553 hours of sunshine in 1893, a figure not exceeded until 1995 ( 1635 hrs) so it was obviously a very sunny year. The totals for 1894 and 1895 were 1114 hrs and 1365 hrs respectively. Kew recorded 1685 hours in 1893 so even allowing for Morecambe's seaside location it does seem a long stretch to reach 2526 hrs.
Record annual sunshine totals are not easy to find, short of going through old volumes of the weekly weather report and adding up the weekly amounts, but somewhere around 2100 hours seems to be in the right area, ie Bognor Regis's total of 2066 hrs in 1933. I'd have thought with Morecambe's north westerly location around 1800 hrs would be the upper limit.
Just found a bit more data relating to this. Between 1941 and 1970 the highest annual sunshine total at Morecambe was 1742 hrs, though it doesn't state which year. The highest annual totals I can find for this period are; Brighton 2068 hrs, Eastbourne 2153 hrs. Worthing2129 hrs, Ventnor; 2172 hrs; Sandown 2256 hrs; Jersey 2291 hrs and Guernsey 2263 hrs.
Is seems very unlikely that any year at Morecambe would record around 300 hrs more sunshine than the sunniest years on the south coast or the Channel Islands even allowing for the different time period.