Although this doesn't help very much with the original question, for the benefit of subsequent discussion the official class allocation definitions currently in use are provided by Rail Industry Standard RIS-2453-RST.
Section A.1 (Table 3) Locomotives and heritage vehicles
(abridged, showing four-digit Class Identifier formatted for display in EVN)
Vehicle Type | [EVN Interoperability Indicator] | [Class Identifier Range] |
Diesel shunting locomotives | 98 | 0001 - 0009 |
Electric shunting locomotives | 97 | See A.1.4 |
Diesel locomotives | 92 | 0010 - 0079 |
Electric locomotives | 91 | 0080 - 0096 |
Existing electrodiesel locomotives | 91 | 0073 |
Heritage locomotives | 90 | 0098 |
A.1.4 Electric shunting locomotive technical characteristics (class identification) numbers shall be selected from the diesel shunting locomotive or the electric locomotive ranges.
Section A.3.1 (Table 7) Multiple unit / fixed formation sets
Rail Vehicle Group | Class Identifier Range |
Diesel mechanical / hydraulic multiple unit sets | 100 - 199 |
Diesel electric multiple unit sets | 200 - 299 |
Diesel and / or other fuels multiple unit sets | 600 - 699 |
DC electric multiple unit sets | 400 - 599 |
AC and AC / DC electric multiple unit sets | 300 - 399
700 - 749 |
Multi-mode multiple unit sets | 750 - 799 |
High-speed multiple unit / fixed formation sets | 800 - 899 |
Infrastructure maintenance / non-passenger multiple unit / fixed formation sets | 900 - 999 |
(where a high-speed unit is one capable of operating at speeds above 190 km/h (120 mi/h))
(where a multi-mode unit is one with more than one source of traction power, of which at least one is external)
On the topic of overlaps between TOPS vehicle numbers and TOPS unit/set numbers - since the establishment of the National Vehicle Register the legal "identity" of a rail vehicle is its European Vehicle Number and not its TOPS vehicle number (referred to as the "GB Operational Number"), although the EVN may include the TOPS vehicle number. The standard includes tables showing the previous and current number ranges for vehicles within multiple units and fixed-formation sets that go towards making up the EVN, but I haven't transcribed them so you'll have to download the standard from the RSSB website yourself (for free) to see them Anyway when taken in full a vehicle's EVN will be very different to any possible TOPS set number.
Using this as an example:
The vehicle number is taken from the 0300000 - 0499999 range current for non-high-speed EMU vehicles, and forms part of the full EVN of 94 70 0465 101-6.
Regarding the Class 777, I suspect they got that because the plans for battery power technically made them multi-mode.