I am with John - brake linings.
On every drum braked landy I have had the same problem.  The gap between the shoes and drums is too great - the first pump of the brakes pushes the linings out and the second push engages the drums.  You say you have new drums then it is the linings. 
If necessary go to oversize linings.  With the snail cams right off (and make sure these are actually engaging the linings), the drums should be a snug but not overly tight fit over new linings.  I had to use oversize linings on my series 1 and series 3 with good drums - in my 101 with first oversize linings the problem was still there with low but in spec drums - needed new drums to fix the issue - when new linings are needed I will need to go to second oversize linings.
As I said the first pump is taking up the slack and the second is working the brakes - so you need to find out why.
Garry
				
			 
			
		 
			
				
			
			
				REMLR 243
2007 Range Rover Sport TDV6
1977 FC 101 
1976 Jaguar XJ12C
1973 Haflinger AP700
1971 Jaguar V12 E-Type Series 3 Roadster
1957 Series 1 88"
1957 Series 1 88" Station Wagon
			
			
		 
	
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