Have you had a look through the TPO Guide to the Law and Good Practice? It lays it all out in simpler terms than the act itself, certainly worth a look. It's dated Pre-2012 regs but the matters for your case are pretty much unchanged.
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/14956/tposguide.pdf
Particular sections useful to you would be:
3.11 During the site visit the LPA officer should gather sufficient information to draw up the TPO with accuracy. The LPA officer should accurately record the number and species of the individual trees or groups of trees to be included in the TPO and their location (see also paragraph 3.14 below). In relation to areas of trees or woodlands it is not necessary for the purposes of the TPO to record the number of trees, and a general description of species should be sufficient. It is, however, important to gather enough information to be able to define accurately on the map the boundaries of the areas or woodlands in question (see also paragraphs 3.15-3.18 below).
From this section I would conclude that even those pesky hollies and spruce are protected, so long as they fall within the outlined area on the order plan. Species information on woodland orders is merely supplementary, and does not infer that only the listed species are protected. The purpose of woodland TPOs is to protect the woodland unit as a whole.
However;
3.16 A woodland TPO should not be used as a means of hindering beneficial management work, which may include regular felling and thinning. While LPAs may believe it expedient, as a last resort, to make TPOs in respect of woodlands they are advised (whether or not they make a TPO) to encourage landowners to bring their woodlands into proper management under the grant schemes run by the Forestry Commission. If, for one reason or another, a woodland subject to a TPO is not brought into such a scheme, applications to manage the trees in ways that would benefit the woodland without making a serious impact on local amenity should be encouraged (see paragraph 6.41 of this Guide).
So you should apply, but as long as your intended works are seen as beneficial to the woodland you should have no issues with refusal.
You can draw up a woodland management plan if you wish, which if sufficiently detailed in terms of work specification and timings can be supplied with one application to cover multiple operations or phases of work over multiple years;
6.41 Only one application is needed to carry out a number of different operations on the same tree (for example, to reduce some branches and lift the crown) or to carry out work on a number of trees (for example, to reduce the crowns of a line of trees). Similarly, a programme of work (such as specific operations which are to be repeated on an annual or regular basis, or a series of operations phased over a period of time) could be submitted as one application. Such applications are in fact encouraged as a means of promoting ongoing beneficial woodland management plans of, say, five years without the need for repeated applications over a relatively short period of time.
Hope this helps