To continue. Bradshaw December 1895 (Middleton reprint), and things start to get a bit more frequent. Note also that Bradshaw does not always distinguish between through trains and connecting services.
1 per hour:
Waterloo - Woking - Ascot
Waterloo - Hampton Court (giving 2 per hour as far as Surbiton)
Waterloo - Effingham Jn - Guildford
Waterloo - Wimbledon - Twickenham
Ludgate Hill - Twickenham via Brixton & Shepherds Bush.
London Bridge - Dorking (or beyond) via East Dulwich & West Croydon
London Bridge - West Croydon via Forest Hill
London Bridge - Victoria via Norwood Jn, Selhurst & Clapham Jn
London Bridge - Victoria via Crystal Palace & Clapham Jn
Twickenham - Gunnersbury.
Shoreditch - Peckham Rye
Shoreditch - New Cross
Liverpool Street - New Cross
Charing Cross - Redhill - Guildford or Reading.
Charing Cross - New Beckenham, continuing (or connection) to Beckenham Jn / Hayes / Croydon (Addiscombe Road)
Charing Cross - Dartford
Crystal Palace (High Level) - Moorgate Street
Victoria - Crystal Palace (HL) via Nunhead
Liverpool Street - Bishops Stortford (connection at Broxbourne for Hertford)
Liverpool Street - Cheshunt via Lower Edmonton
Liverpool Street - Stratford - Chingford
North Woolwich - Palace Gates
Gospel Oak - Chingford (with Stratford connection at Walthamstow St. James Street)
Liverpool Street - Ongar via Stratford & Loughton
Finsbury Park - Muswell Hill.
Willesden Jn - Victoria via Kensington Addison Road.
Euston - Watford with connections Harrow - Stanmore & Watford to Rickmansworth & to St. Albans
2 per hour:
Clapham Jn - Kensington Addison Road (now called Olympia)
Victoria - West Croydon via Clapham Jn
Liverpool Street - Ilford (one continued to Shenfield)
Liverpool Street - Chingford
Fenchurch Street - Blackwall
Fenchurch Street - Barking (1 each continuing to Shoeburyness or Tilbury)
Liverpool Street - Seven Sisters (2 each continuing to Enfield Town or Palace Gates (Wood Green))
Broad Street - South Acton (then one each to Richmond or Hammersmith)
Broad Street - Kensington Addison Road, continuing as through trains or connections via District line to Mansion House.
Broad Street - Finsbury Park
Kings Cross - Finsbury Park (as part of other listed services)
Finsbury Park - High Barnet (originating at Victoria or Broad St.), one with Edgware connection.
Finsbury Park - Enfield (originating at Broad St. or Moorgate St.)
Moorgate Street / Kings Cross - New Barnet
Baker Street - Harrow on the Hill (one continuing to Rickmansworth)
(I have not listed other Metropolitan Railway services which were then steam, but later became LT / LU electric lines), but 2 per hour seems fairly typical.
Paddington - Slough (one from Bishop's Road, which became the "suburban" platforms at Paddington), plus one Slough - Reading connection, and one Paddington - Maidenhead (Semi-fast to Slough then all stations.)
3 per hour:
Charing Cross - Greenwich - Woolwich
Victoria - Bromley (or beyond). (1 connection per hour Holborn Viaduct - Loughborough Jn, plus 1 per hour St. Paul's to Loughborough Jn.)
Victoria - Kings Cross (Met.) via Brixton & Moorgate Street. (2 continued to Kentish Town (MR), the other to Kings Cross GNR. Supplemented by 1 Clapham Jn to Moorgate Street, and another between Loughborough Jn & Kentish Town (MR)
Fenchuch Street - Forest Gate / Ilford
4 per hour:
Waterloo - Putney (one each hour extending to Shepperton, Feltham via Hounslow, Windsor & Kingston.)
London Bridge - Battersea Park (one extended to Victoria)
Broad Street - Chalk Farm (or beyond)
Broad Street - Poplar
Fenchurch Street - Custom House & Gallions (either as through trains or connections)
Some continued to North Woolwich, which with a Liverpool St. - North Woolwich service gave 3 per hour between Custom House & N. Woolwich)
End of 1895 services. Will probably be a few days before I have time for any more.