Fredericks age in 1940 was 23 and it just says 'Soldier' as his occupation.
May have a possibility, if that age is right.
Best matching birth reg is
March 1917 Chorlton 8c 1266 
Wilcock, Frederick    mother Bailey   
There's a possible sibling registered in Chorlton in the 
June quarter 1914,  John Thomas Wilcock, mother Bailey
Possible death? 
June 1943 Blackpool 8e 705
Wilcock, Jonathan    
age 78   
Probate in 1943, Jonathan Wilcock of 5 Squires Gate Lane Blackpool, 
executor is Annie Wilcock, widow
https://probatesearch.service.gov.uk/Calendar?surname=wilcock&yearOfDeath=1943&page=2#calendar
Same address - is this Jonathan's daughter-in-law & son
Nelly Wilcock of 
5 Squire Gate Lane Blackpool (wife of 
John Thomas Wilcock) 
died 18 August 
1938 King George V Hospital Valetta Malta
Administration 22 Apr to said JTW telegraphist R.N.
marriage 
John T WILCOCKSep 1935 Fylde Lancashire
Spouse:   
Nelly WOODVolume Number:   8a Page Number:   2061
Edit
Mrs Nellie Wilcock Age:   23, housewife
Departure 21 Nov 
1936Port of Departure:   Southampton
Destination Port:   
MaltaShip Name:   Largs Bay
Last address in UK  
2 Welch Road Gosport Hants