The UK did not delay the programme, a lot of time was lost in 1992/3 when Germany quit the project for a time.
While a Commons committee found that had the project been an all UK programme, costs and time would have ended up being reduced as things turned out, the fact is the initial costs of a national programme would have likely killed it when the Cold War ended.
As to this spurious 'out of date' argument, can we honestly say that during the 25-30 year service life of the aircraft, a potential opponent definitely will not appear with agile fighters?
In any case, the aircraft has for a long time been envisaged as being more multi role than the press seem to think, as early as the mid 80's, RAF planning had the aircraft replacing strike/attack Jaguars as well as Phantoms and Tornado F.3s.
Tranche 2, now ordered, will be more multi role.
If Typhoon is out of date, not needed in world where no enemy will be able to challenge in the air to air environment, then so is F-22 and Rafale.
F-35 is primarily a strike fighter, with decent air to air capability, a much later design that will not be available until after the end of this decade.
F-35, as JSF, came out of a need to replace a range of US aircraft, F-16, F-18, AV
-8B, unlike the Cold War one aircraft would have to replace all, such were the realities of the post Cold War world.
In RAF/RN service, the VSTOL version will be a Harrier replacement, maybe some RAF spec, land based, F-35C's could be part of a Tornado GR
.4 replacement, along with probably an undefined as yet UCAV
, but don't rule out Tranch 3 Typhoons being part of this as well.