Insert landscape page after paragraph x

I’d like to insert a landscape page (with a figure on) the page after a certain paragraph (so if page 2 has this paragraph on, I’d like page 3 to be landscape). I can do that with page breaks, but if I add any text to the beginning of my document I have to reposition the page break every time.

Is is possible to get the text to sort of jump past the extra page?

A less good alternative would be to increase the page number (in the footer) by 2 insead of one, only on the page that this paragraph is on.
And then have the extra page (with correct number) at the bottom.
So then page 2 has the paragraph on page 3 is the next portrait page and labelled ‘4’, the last page is landscape and labelled ‘3’.

Hope that makes sense…

I am not entirely certain I understand. Inserting a page break with the required page Style (Landscape) should do what you require i.e., cause the content on the current page to cease and jump to the next page (a page using Landscape orientation). If you insert enough additional content prior to the page break to cause the page break to jump to the next page then you will get the remainder of that new page appearing blank. This is normal behaviour for breaking content.

If on the other hand you wish to have the content flow over pages with different page styles then a pair of linked page styles (via Next Style) will be required. It does not sound like this is what you require though.

Neither. I’ll have another go at explaining it. I want the content to flow over all portrait pages, but I want a landscape page after a paragraph (the lanscape page contains a picture, and the paragraph references it)

This is exactly what a page break with alternate page style will do. Prior content will flow over portrait pages and then, after the final paragraph (wherever it falls on the page), jump to the landscape page. I generally prefer however to rotate my artwork counterclockwise rather than the page as the head/foot get rotated with the page. There is currently no elegant way around the head/foot issue other than text boxes or turning the head/foot off for the landscape page.

Ah! I’ve worked out what you meant by linked page style, but it’s still not quite doing what I wanted.
Now I can e.g. make page 3 landscape and then page 4 goes back to portrait, but if I go back to the first page, and press return loads of times, the landscape page stays on page 3 rather than following the paragraph that it was made from - when that paragraph moves to page 5 I would like the landscape page to be on page 6.

What you describe is correct behaviour for linked page styles. To get the first change of page orientation to remain fixed after a given paragraph you must use a page break with associated style. I have stated this several times. We can’t really discuss this any further here in the comments as the FAQ stipulates the site is not for discussions. All I recommend is you re-read my answer.

I am also not sure if I understand your question and task very well. But let me give you some additional hints from my point of view; however please read also the answer of @owen carefully.

Have a look at

Changing Page Orientation (Landscape or Portrait) - LibreOffice Help

and read especially

Manually Defined Range of a Page style