Difficult to beat the Class 89 - only one built and it has been preserved. Likewise Duke of Gloucester
8203, 8233, 8237, 8243, numbered ADB968003/001/002/000 in that order
HST have examples of every class from 01 to 09
That would be terribly confusuing, as the original 13101 still exists, (later D3101, no TOPS number carried as it was sold into industrial use in 1972)
That's the electric APT-P - "P" for pre-production (class 370). I understand the OP meant the gas-turbine powered APT-E (for experimental), which is now in the NRM at Shildon, which carried a few [passengers on demonstration runs but never went in to revenue service (or received a TOPS class)
The class 44s haven't done badly at 20% (two out of 10)
Officially that was two units (albeit they usually ran as one train)
Taking "rare" as being 25 or fewer examples built, but disregarding class 59 as they are all still in service
Class 118 (triple) 0.3/15 (2%) one power car preserved
Class 106 (twin) 0.5/14 (4%) All converted to class 105, one driving trailer preserved)
Class 06 1/25 (4%)
Class 81 1/25 (4%)
Class 71/74 1/24 (4%)
Class 28 1/20 (5%)
Class 83 1/15 (7%)
Class 82 1/10 (10%)
Class 84 1/10 (10%)
Class 202 (hex) 2/9 (11%)
Class 103 (twin) 2.5/20 (12%)
Class 44 2/10 (20%)
Class 109 (twin) 1/5 (20%)
Class 48 1/5 (20%) converted to, and preserved as, class 47
Class 207 (triple) 4/19 (21%)
Class 55 5/22 (23%)
Class 77 2/7 (29%)
Class 201 (hex) 2/7 (29%)
Class 02 7/20 (35%)
Class 122 7/20 (35%)
Class 07 5/14(36%)
Class 121 6/16 (38%)
Class 01 2/5 (40%)
Class 41 (HST) 1/2 (50%)
Class 403 (quin) 2.8/3 (93%) All fifteen cars originally preserved, but one subsequently written off in a fire.
Class 89 1/1 (100%)
Class 140 (twin) 1/1 (100%)
No examples preserved
Class 112 (twin) (25 built)
Class 113 (twin) 25
Class 111 (twin/triple) 24
Class 29 20
Class 125 (triple) 20
Class 16 10
Class 23 10 (one replica under construction)
Class 123 (quad) 10
Class 128 10
Class 124 (hex) 8.5
Class 203 (hex) 7
Class 41 (NBL) 5
Class 251 5
Class 13 3
Class 70 (SR) 3
Class 129 3
Class 210 2 (one DTSO preserved)