The Nimrod design retained the Comet fuselage and added the weapons pannier so that the crew area would not be compromised. The two prototypes used unfinished Comet airframes.
Designs were made using just about every British multi-engined aircraft in production at the time, though a jet aircraft was always preferred over a turboprop. I think the Air Staff Requirement that led to the Nimrod specified jet engines, though I remain to be corrected on that. Hawker Siddeley also offered a Maritime Trident, though later concentrated on the Maritime Comet. BAC offered variants of the One-Eleven and the VC10, though the One-Eleven was always an outsider as it only had two engines.
A lot of it came down to cost and capacity. Hawker Siddeley at Woodford had the capacity to build the Nimrod, while BAC at Weybridge were already working on the VC10 and would not have had the capacity to build a maritime version. It would also have been more expensive.
There is a lot more to it of course, but that is the basics of the answer.