There is a good nest and egg book but it is old, etiquette around studying and photographing nests and eggs has changed over the years. The book is Nesting Birds Eggs and Fledgelings in colour pub Blandford By Winwood Reade and Eric Hosking.
I will be very interested to see what you find on Thursday and I am going to plump for Linnet. Simply on the view of the habitat I would reckon I would be far more likely to see linnet there than greenfinch, bullfinch which are not really open heathland birds or yellowhammer which I would expect in more open country. Having checked the pics in Hosking's they fit pretty well bang on, the only other eggs which look very close are twite and siskin which we can rule out on region and habitat. The description of nests (he used to study huge numbers of nests) was bang on too.
"breeds mid april-aug, on rough ground with bushes, frequently on commons with gorse and thorn scrub, also in young plantations, hedgerows, gardens occasionaly on dunes and in heather. Nest usually in a bush or hedge, but also on banks and in low vegetation, such as heather, tufts of grass and rush.Female builds substantial structure of grass and moss, (and here is the clincher) lining it with hair, wool, fur and ocasionally feathers. eggs 4-6 bluish white with dark markings, incubated chiefly by female for about 1 1/2 weeks. Nestlings greyish down pink inside mouth pale pink flanges, fed by both parents. leave nest after 1 1/2 weeks.
Hints constant twittering song usually attracts attention. Male displays by drooping wings and spreading tail. If you squat down whilst searching you will have more chance of seeing the nest silhouetted as it is often towards the top of a bush or hedge.