Hi Kev,
Well, I guess Exeter Place is highly likely! Being, as you say, off Derwent St - as can be seen on Street Map UK! That scribe certainly has much to answer for in his writing! There is an Eagle Street in Derby but I think that Exeter Pl is very much more likely!
And I'm so very very glad that the Tunaley website I referred you to has turned out to be totally relevant!
As Marcus TUNALEY (the "poor guy"!!) says on his site, he thinks that all TUNALEYs are related! Which seems very likely indeed.
And, as you've no doubt seen, many of the TUNALEYs were Dyers.
Have lots and lots and lots of fun.
All the very best,
JAP