Acquired by McPhee sometime after the recording of Hogwash and used for The Two Sides of Tony (T.S.) McPhee and Solid. It is specified in a November 1974 Beat Instrumental interview and is corroborated by the following:

Sounds, May 5, 1973, "Mac’s Home Cooking: The Groundhogs" by Jerry Gilbert

Tony started building the studio in January, the centrepiece being an eight track console which he’d procured from the De Lane Lea studios in Kingsway. As a technician for whom nothing less than the right sound is sufficient, he made up his mind that Hogwash would be the last album the Groundhogs would record in London.

[...]

"Studios really piss me off so I wanted to get my own studio done because it was necessary", McPhee blandly pointed out. "It started off as a four-track and then became eight when I got this equipment."

Beat Instrumental, November 1974, "Home Studios: Tony McPhee" by Del Robinson, pgs. 28

Tony certainly has plenty of opportunity to develop his engineering now. For a start, the centrepiece of the crowded control room is the Cadac 8-track desk, which he bought second-hand from Majestic Studios in Clapham. 'It can be converted very easily to 16.' This is the second desk Tony's installed in his home studio. 'I did a deal with De Lane Lea, before they became Kingsway Recorders, and bought about £5,500 worth of gear, which was the basis of a complete studio.

'I used the original desk to do my solo album, but it didn't have the advantage of pan pots, so when this one came up I decided to take it. I've ordered an Ampex 16-track recording machine which I should be getting very soon.'

At the moment Tony's using the 3M eight-track machine he acquired from De Lane Lea, linked up to the 'garage' by remote control. He also has a Revox which he uses mostly as an effects machine — 'I've got a Varipitch as well and I can use them for automatic double tracking and phasing. I can take a signal out from the guide head of the eight-track machine, pass it through the Revox and mix it in with the playback head. I can then use it for phasing, editing, or playing echo — it's a very handy thing, especially on an eight-track machine, when you can't afford to use just one track for double tracking.'

Rock's Backpages audio, "AUDIO: The Groundhogs' Tony McPhee (1997)" by John Tobler (@ 53:38)

Tony "T.S." McPhee: So, by that time, I'd got equipment, 'cause my idea was it's cheaper to buy the equipment. Then you can, from that point, you can have as many albums as you'd like. Yeah.

John Tobler: Yeah. You mean recording it?

McPhee: Recording from it, yeah.

Tobler: Okay.

McPhee: So I actually bought out De Lane Lea... a eight-track,

Tobler: Yeah.

McPhee: which is what we did Thank Christ and Split on.

Tobler: Oh.

McPhee: And other assorted bits and pieces. And so, from that point on, I did my own albums. We did— I did Solid out there. [...] and built out to a sixteen-track. So, Solid was eight-track and then, uh... yeah, Crosscut Saw and Black Diamond were both on sixteen.

Although the model is unspecified, it can be deduced from the following:

1. The M23 was released in 1966.
2. In the November 1967 issue of Beat Instrumental, it is reported on page 14 that "DE LANE LEA have an eight track machine on order and hope to have it in operation before January."
3. The sixteen-track prototype of the eight-track-capable M56 was not unveiled until the 35th Audio Engineering Society (AES) Convention in October 1968, as attested by engineer C. Dale Manquen's paper for the event.
4. The June 1969 issue of Beat Instrumental quotes De Lane Lea's chief engineer, Barry Ainsworth, on page 24 saying "The equipment we have here consists of an 8-track machine, made by the 3-M company, and a new type of amplifier, our own design, half the size of the normal. We also have 4- and 2-track Ampex machines as well as mono."
5. The March 1970 issue of Beat Instrumental reports on page 23: "Equipment at Kingsway includes an 18-channel 8-track console, custom-built by Sound Techniques, which was also responsible for the electronics of the 8-track tape machine, which has a 3M deck. In addition, there are Ampex four-track, two-track and mono machines and an EMI mono."
6. The May 1970 issue of Beat Instrumental reports on page 12: "At De Lane Lea's Kingsway studios, the Groundhogs were putting finishing touches to their album".
7. In its preview of the 1972 Association of Professional Recording Studios (APRS) exhibition, it is reported on page 49 of the July 1972 issue of Studio Sound that "3M will feature a 16 track version of the new M79 designed by their Mincom division." This shows that the eight-track-capable M79 was still new at this time, thus postdating De Lane Lea’s 1967 order.
8. On page 328 of Recording the Beatles: The Studio Equipment and Techniques Used to Create Their Classic Albums (2006) by Kevin Ryan & Brian Kehew, while discussing the recording of "It's All Too Much" at De Lane Lea in late May 1967, it is stated parenthetically that "DeLane Lea would later acquire a 3M 8-track , the same model chosen by EMI". According to Brian Gibson (here, here and here) and Ken Scott, the eight-track 3M tape machine at EMI was an M23.