Appreciate this isn't 1988, but shows what it was like within a few years.
One of the substantial changes in 1990 was Solent Link electrification, which led to the additional Portsmouth Harbour via Eastleigh services.
To show that, Summer 1989 is somewhat different from what is posted above, but closer to 1988
From the public timetable, 1989 had, from 1600 to 1900
1605 Southampton, calling at Clapham Junction, Surbiton, Woking and all stations to Southampton
1610 Alton, calling at Surbiton, Walton-on-Thames, Weybridge, West Byfleet and all stations to Alton
1615 Basingstoke, calling at Clapham Junction, Woking and Basingstoke
1620 Portsmouth Harbour, calling at Clapham Junction, Woking, Guildford and all stations to Portsmouth Harbour
1622 Guildford, calling at Clapham Junction, Wimbledon, Surbiton and all stations to Guildford via Woking
1632 Weymouth, calling at Southampton Airport, Southampton, Brockenhurst, Bournemouth and all stations to Weymouth
1635 Eastleigh, calling at Clapham Junction, Wimbledon, Surbiton, Woking and all stations to Eastleigh
1640 Salisbury, calling at Clapham Junction, Basingstoke and all stations to Salisbury
1645 Poole, calling at Clapham Junction, Woking, Basingstoke, Winchester, Eastleigh, Southampton Airport, Southampton, Totton, Brockenhurst, New Milton, Christchurch and all stations to Poole
1648 Alton, calling at Woking and all stations to Alton
1650 Portsmouth Harbour, calling at Guildford, Haslemere, Petersfield, Havant, Portsmouth & Southsea and Portsmouth Harbour
1652 Farnham, calling at Clapham Junction, Wimbledon, Surbiton and all stations to Farnham
1658 Portsmouth & Southsea, calling at Woking, Guildford and all stations to Portsmouth & Southsea
1700 Southampton, calling at Woking, Farnborough and all stations to Southampton
1705 Exeter St Davids, calling at Basingstoke, Whitchurch, Andover, Salisbury, all stations to Honiton, Exeter Central and Exeter St Davids
1708 Portsmouth Harbour, calling at Woking, Worplesdon, Guildford, Godalming, Haslemere, Liphook, Liss, Petersfield, Havant, Bedhampton, Fratton, Portsmouth & Southsea and Portsmouth Harbour
1710 Guildford, calling at Wimbledon, Surbiton and all stations to Guildford via Woking
1715 Weymouth and Poole, calling at Winchester, Southampton Parkway, Southampton, dividing for Bournemouth, Poole, Wareham and all stations to Weymouth, and for Totton, Lyndhurst Road, Brockenhurst and all stations to Poole
1718 Alton, calling at Woking and all stations to Alton
1720 Portsmouth Harbour, calling at Woking, Guildford, all stations to Havant, Fratton, Portsmouth & Southsea and Portsmouth Harbour
1724 Eastleigh, calling at Woking, Farnborough, all stations to Basingstoke, Winchester, Shawford and Eastleigh
1726 Farnham, calling at Surbiton and all stations to Farnham
1730 Bournemouth, calling at Woking, Basingstoke, Micheldever, Winchester, Southampton Parkway, Southampton, Brockenhurst, New Milton, Christchurch and Bournemouth
1732 Portsmouth Harbour, calling at Woking, Guildford, Godalming, Haslemere, Petersfield, Havant, Bedhampton, Fratton, Portsmouth & Southsea and Portsmouth Harbour
1734 Yeovil Junction, calling at Farnborough, Fleet, Basingstoke and all stations to Yeovil Junction
1736 Basingstoke, calling at Walton-on-Thames, Weybridge, West Byfleet, Woking and all stations to Basingstoke
1740 Portsmouth & Southsea, calling at Woking and all stations to Portsmouth & Southsea
1743 Farnham, calling at Surbiton and all stations to Farnham
1745 Weymouth, calling at Woking, Basingstoke, Winchester, Eastleigh, Southampton Parkway, Southampton, Totton, Brockenhurst, Bournemouth, Branksome, Parkstone, Poole, Hamworthy, Wareham and all stations to Weymouth
1748 Alton, calling at Brookwood and all stations to Alton
1750 Portsmouth Harbour, calling at Woking, Guildford, Godalming, Haslemere, Petersfield, Havant, Fratton, Portsmouth & Southsea and Portsmouth Harbour
1754 Poole, calling at Woking, Farnborough and all stations to Poole
1756 Haslemere, calling at Surbiton and all stations to Haslemere via Woking
1758 Haslemere, calling at Worplesdon and all stations to Haslemere
1800 Poole, calling at Woking, Basingstoke, Micheldever, Winchester, Eastleigh, Southampton Parkway, Southampton, Brockenhurst and all stations to Poole
1805 Basingstoke, calling at Clapham Junction, Woking, Farnborough and all stations to Basingstoke
1808 Guildford, calling at Surbiton, all stations to Woking, and Guildford
1811 Portsmouth Harbour, calling at Woking, Guildford, Godalming, Haslemere and all stations to Portsmouth Harbour
1815 Exeter St Davids, calling at Woking, Basingstoke, all stations to Feniton, Exeter Central and Exeter St Davids
1815 Portsmouth Harbour, calling at Clapham Junction, Wimbledon, Surbiton and all stations to Portsmouth Harbour
1818 Alton, calling at Woking, Ash Vale and all stations to Alton
1820 Basingstoke, calling at Surbiton, Woking, and all stations to Basingstoke
1827 Portsmouth Harbour, calling at Woking, Guildford, all stations to Havant, Hilsea and all stations to Portsmouth Harbour
1832 Weymouth, calling at Winchester, Southampton Parkway, Southampton, Brockenhurst, Bournemouth, Poole and all stations to Weymouth
1834 Alton, calling at Walton-on-Thames, Weybridge, West Byfleet and all stations to Alton
1840 Salisbury, calling at Basingstoke and all stations to Salisbury
1842 Basingstoke, calling at Clapham Junction, Surbiton, Woking and all stations to Basingstoke
1845 Guildford, calling at Clapham Junction, Wimbledon, Surbiton and all stations to Guildford via Woking
1850 Portsmouth Harbour, calling at Woking, Guildford, Godalming, Haslemere, Petersfield, Havant, Fratton, Portsmouth & Southsea and Portsmouth Harbour
The 1715 was "The Royal Wessex". The 1650 was "The Victory"