They're turbojet engines, not the turbofans that you see today.
Turbojets have a smaller intake and the entire thing produces thrust. Unlike today's much more efficient turbofans, where a small turbojet turns the larger fans to produce most of the thrust.
In the early 2000s, BAe Systems had a project in train to upgrade them to the MRA4 spec, essentially remanufacturing the existing MRA2/MRA3 Nimrods around a new wing structure that could accommodate RR BR700 turbofans, doubling the aircraft's range:
(Go look at the photos on the respective wikipedia pages and examine the engine inlets at the wing roots: the MRA4's air intakes are much larger.)
The MRA4 upgrade was at least as radical as the proposal to re-engine USAF B-52 bombers with four GE high-bypass turbofans (as seen in the photograph on the web page below, showing a B-52 flying with the new engine in the inboard starboard pod):
... Which also got cancelled; in the case of the B-52 the USAF had so many old engines in mothballs that re-engining the B-52 would cost more than just swapping out old units, and in the case of the Nimrod MRA4 the program ran into nightmarish cost-overruns when it became apparent that the aircraft they were trying to remanufacture were all different — the RAF's Nimrod fleet had been hand-built then patched for half a century and simply couldn't be consistently upgrades.
(Moral of story: upgrading a 50+ year old design is harder than it looks.)
They were supposed to have finished their sea trials by now.
Also they were supposed to be convertible to cats & traps at the drop of a hat, which would have allowed the UK to procure a non-BAe fighter to fly off them, couldn't have that...
FWIW, other turbojet airliners had larger intakes. E.g Tu-104 (which, coincidentally, was propped by Comet's fall, becoming the only jet airliner in service for a couple of years):
Compact turbojet engines rather than high-bypass turbofans like modern airliners. Blended into the wing for less drag compared to underslung wing pods like the contemporary rival 707.
But what's striking, and indeed rather UFO-like, are the small engine intakes. Anyone know what's up with that?