MRA4 didn't have "computer designed wings" - it certainly had wings designed in CAD rather than by drawing with quill pens on stretched velum, but the outcomes would have been similar by either method. There were some problems with the wing design, but that wasn't one of them
As for the engines - it wasn't so much the long ducts as the close proximity of the engines that was the problem. No one had ever run turbofans with that high bypass ratio that close together, and so when the detailed design analysis was done they discovered that they "fought" each other for intake air, severely reducing thrust at higher power settings. This SHOULD have been discovered during the "Risk Reduction contract" phase of the procurement process - MoD's own written process said as much. The RR phase is an initial contract to explore any areas of high technical risk and mature them ahead of the main design process so that the overall risk exposure us smaller - it's a rational approach to managing technical risk, and it was legally mandated at the time.
But this contract was coming up towards the end of an increasingly unpopular conservative government which was desperate to place some government orders to buy a handful of votes. Two projects were purchased "prematurely" as a result - the order for Apache attack helicopters and the MRA4 contract. The then MinD (Micky Portaloo) didn't want to place a teensy-weensy £120m 18-month risk-reduction contract just so that his successor could get the credit for placing the £2.1bn main development contract, so he went hardball with a single "fixed price" development and production contract. BAES then compounded error by accepting the contract (rather than refusing to play ball as they subsequently did with the QEC contract), and so a fixed-price non-de-risked project was initiated which both sides knew full well would never be able to run to the defined schedule even if there were no snags. And of course there WERE snags - mistakes, requirements creep (well, "gallop" would be closer to the mark), political interference etc etc.
And the rest is history...
PDR