From December, the Hertford North / Welwyn GC trains, which currently
get diverted to Kings Cross late night and all day at the weekends, will
serve Moorgate 7 days a week, although a few very early and very late
trains will still use Kings Cross.

http://assets.goaheadbus.com/media/c...services. pdf

Also, c2c will be running some trains via Stratford to Liverpool Street
all day long at the weekend, as well as some to Fenchurch Street. The
Dagenham Dock line, whose Sunday service currently consists of an hourly
shuttle between Barking and Grays, will have a half hourly service to
Fenchurch Street.

http://www.c2c-online.co.uk/media/79...rom-london.pdf