Taken from the illuminated roll of honour in Blackham Church
If you know of other people who should be included, please let me know
(underlining indicates a link to a page with further information about that person)

Lt Col D P Haig OBE Garrison Btn Scottish Rifles     French E Royal Sussex Regt  
Major L C Ludlow 5th Btn Royal Sussex Regt   Gasson T Royal Sussex Regt Wounded
Capt J C Ludlow Royal Inniskilling Fusiliers Killed Gill J    DCM   Killed
Lt R P Haig 5th Cameron Highlanders Wounded Groombridge J T Royal Sussex Regt Killed
Lt J Kestin Seaforth Highlanders Wounded Haddon J Motor Transport  
Allen A East Surrey Regt   Haddon H Kings Royal Rifles  
Atheral W Royal Sussex Regt   Harding E Royal Sussex Regt  
Baldwin C Royal Sussex Regt Killed Lewis J F 3rd Welch Regt  
Baldwin W Royal Sussex Regt   Mann A Royal Navy Drowned
Barker W H T Royal Navy   Maplesden J Royal Sussex Regt  
Bashford G Royal Sussex Regt   McMaster J Royal Sussex Regt  
Booker A Royal Field Artillery   Miles H East Surrey Regt  
Buckwell W 7th Northumberland Fusiliers Wounded Munns F Royal Engineers  
Childs F Sherwood Foresters Killed Peerless G   MM Royal West Kent Regt Wounded
Collins J Royal Sussex Regt Wounded Peerless J Royal West Kent Regt Wounded
Collins T Royal Sussex Regt   Peerless H Royal Navy  
Collins Nelson Royal Sussex Regt (Killed) Peerless H Kings Royal Rifles  
Cottenham J Royal Sussex Regt   Reed P Royal Fusiliers Wounded
Cottenham T Royal Sussex Regt   Tester H East Surrey Regt  
Cross W Royal Navy   Thomas F Royal Sussex Regt  
Crowhurst W R Royal Navy   Towner F sen Royal Garrison Artillery  
Crowhurst J Royal Navy   Towner F jun Royal Navy  
Daughtrey J Royal Engineers   Towner I RN Vol Reserve Died in Service
Farnes W Royal Sussex Regt   Wickham W sen Royal Sussex Regt  
Floyd T 5th East Kent Regt   Wickham W jun Royal Sussex Regt  
Ford W L Motor Transport   Wallace H 8th Royal Sussex Regt  
French H 23rd Cheshire Regt   Wood M Royal West Kent Regt Killed

The following men appear on the War Memorial on Blackham Church gate
but not on the roll of honour inside.
That may be because the war memorial was made after the roll of honour
by which time the village had learned of more men who had given their lives

Divall, F T Royal Sussex Regt Killed   Sales, A H Royal Garrison Artillery Killed
Miles, J Royal Engineers Killed   Stonley, E W 11th Hussars Killed
Reed, R G Australian Imperial Force Killed        

Then there are men with Blackham connections who don't appear on either the roll of honour or the lychgate memorial

Royal Sussex Regt
Killed
 
Royal Sussex Regt
 
Canadian Expeditionary Force
         
Royal Engineers
   
Royal West Kent Regt
Wounded

Thanks to Sheila Wellstead for the photographs on which this is based