I mostly visited the BML in the 1985-88 period so can supply some details about that era - from memory only, sadly no timetables or CWNs.
The main difference from 1981 was the introduction of Gatwick Express of course, on the quarter-hour as post-privatisation. A knock-on effect was the reduction in stopping services from Victoria (the former Rapid City link services), down to 2tph from 4tph, so that by 1985 there was only one Brighton stopper and one Horsham stopper per hour (some hours going to Littlehampton). To compensate, the Bognor semi-fast called additionally at Ifield and Littlehaven, and no longer carried a Portsmouth portion. This now worked via Hove and was detached off the Littlehampton service.
So approximate times (based on memory, might be two or three minutes out) from Victoria in 1985:
00, 15, 30, 45 - Gatwick Express
02 - Brighton fast, still only East Croydon
06 - Bognor semi-fast via Quarry and Horsham
10 - Brighton stopper
21 - Littlehampton and Portsmouth via Hove. Divided Worthing, I think
24 - East Grinstead and Uckfield, still Thumpers, divide at Oxted
32 - Brighton semi-fast, much as in 1981, I think
40 - Horsham stopper, some hours extended to Littlehampton. Only this served Christs Hospital and Amberley, thus these stations had irregular service during the day
51 - Hastings via Eastbourne (no longer working to Ore)
In contrast to 1981, Clapham Junction stops featured in all services except the xx02 Brighton fast, and, presumably as it would slow up the GatEx 6 minutes behind it, the Oxted Thumper.
No London Bridge fasts this year.
In addition there were two suburbans per hour from London Bridge to Redhill and to Reigate, which provided the service at Coulsdon South and Merstham. I never saw these (as my two visits in 1985 were to Brighton and Clapham) but they were marked 2nd-class only in the timetable and thus presumably were EPBs and/or 455s. Also they were slightly off perfect clockface 30 min interval, and I think one went via Forest Hill and the other via Crystal Palace.
In 1986, broadly the same pattern applied but one tph was added back. The xx10 and xx40 (ish) both became Horsham stoppers, and to compensate for the lost Brighton stopper, an additional xx03 London Bridge to Brighton was introduced, combining with the xx32 Victoria to produce a roughly half-hourly service at Burgess Hill, Hassocks etc. In contrast to its mostly VEP-operated predecessor this was operated exclusively with CIGs. Also, as a result of 2 Horsham stoppers per hour being restored, the Bognor semi-fast lost the Ifield and Littlehaven stops again.
Also in 1986 the Oxted Thumpers moved to xx36 out of Victoria.
Finally in 1986 the two suburbans mentioned above were removed, with Coulsdon South and Merstham now served by the Horsham stoppers.
No changes in summer 1987, IIRC, but in autumn 1987 the East Grinstead electrification occurred and 2tph was introduced on the Oxted line. Out of Victoria the xx36 departure time was maintained, and the use of EMUs permitted a previously-absent Clapham stop, while the second tph was xx09 out of London Bridge (so London Bridge had two fasts within six minutes of each other then nothing). Meanwhile Uckfield became an Oxted shuttle.
In summer 1988 Thameslink was introduced with 2tph. One effectively replaced the xx03 London Bridge to Brighton, while the other terminated at Gatwick Airport. Also the xx09 London Bridge-East Grinstead called additionally at Norwood Junction and left xx07.
Also, another feature of both this era and the early 80s was the closure during off-peak hours of Earlswood and Salfords.
Yes, that would have been when the Croydon area resignalling and layout changes happened with the complete remodelling of services between Selhurst / Norwood Junction and Coulsdon and rebuild of Windmill Bridge Junction.
Yes, that's come up before on here I think. Oddly the 1981 CWN (with no such amendments) has validity date until May 1982, while the ABC timetable (dated Nov 1981) has already had the amendments applied.