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Terminals C and E are now connected airside, so if you are HBO and with a boarding pass then you can walk to the next building along, C, enter security there and walk all the way around to the E gates. The BA lounge is right on the end of this pretty long walk. You can do it landside too, C merges into E eventually.
If you have to go to the E check-in area then the most direct route is via the central car parks, it is signposted but you need a good sense of direction. There is also a bus transfer between terminals too.