Moving in gift

Depends a bit on price maybe? Flower seeds or garden centre voucher
Subscription to a a magazine on home decoration
Gift voucher from suitable shop
Thinking these would take up no space in luggage where as a present would

I think it's always nice to arrive with a gift in hand, but I do love your idea of a delivered bouquet. I'd be tempted to send the bouquet the day before you arrive saying you're looking forward to seeing them and their lovely new home.
Afterwards might be a little like you forgot to get something. But only in my humble opinion.

Snowdrop bulbs are tiny and wouldn't take up much space in your bag.

If your friends aren't gardeners, maybe some lavender bags or scented drawer sachets?

I usually send flowers afterwards to say thank you.
When buying a present I tend not to buy anything for the home that may not be their taste. Maybe a luxury scented candle. If you have a National Trust shop close they may have something suitable.

Lavender bags sounds nice too.

If you are flying to anywhere outside your own country, check with Customs that you can take seeds or bulbs - often they are banned in the country you are flying to.

If you can't buy something once you get there, a nice vase, well wrapped in all your packed clothing, might work.

Be careful with bulbs and seeds if you are flying obviously depends where you are flying to but they are banned in some countries

Sorry Bradfordlass I ve duplicated your warning

A book is always a good shape to stash in a suitcase. Maybe a visitors book so that they can record happy memories of their friends' visits. If there's time maybe you could get it personalised, e.g. with the new address embossed on the front.

Do they have a number/name plaque for the new house

I was just discussing delivered bouquets with a friend the other day. We both dislike them because they are expensive and you just see them deteriorate every day.

If I were your friend I would like a garden centre voucher so I could choose my own gift.

I'm not sure about number plaque. Or vase. Personal taste. I remember a friend telling me she would only ever use plain glass vases, which is not what I would have chosen for her.
If I was giving a gift token I would send it after the visit. It would be odd (imo) to give one on arrival.

When good friends moved into a new house (a flight away from us), we sent a few David Austin rose bushes. They still talk about them and point them out when we visit. However, I know that I would like to arrive with a gift when going to stay. Maybe a bottle of fizz from the airport on arrival and then follow it up with a delivery of a few plants for the garden after you’ve gone?

Towels! (I know I've said this before on GN, for wedding gifts, but I think that they can make a great "new home" gift, as well.) In this case, perhaps one or two pretty, good quality, hand towels - these wouldn't take up that much room? Could be squashed into your luggage?

One of those boot scrapers. If they've built their own house it will be muddy!

It depends where they live but I think I would try and stick to gift vouchers. Recently I gave my friend one of my watercolour paintings for her home and she was really pleased with it. Maybe a piece of local art. Also how about adopting a donkey for them, just a thought.
www.thedonkeysanctuary.org.uk/adopt?ds_rl=1249597&gclid=Cj0KCQjw6IfoBRCiARIsAF6q06sfuow8Hth613Sy7iq_xdbZXH44KoPLz1G3jwCrG0rPCr_ZcxAzdYsaAlyxEALw_wcB&gclsrc=aw.ds

I like a fragrant climbing rose rather than a bouquet, it doesn't need much room and lasts forever.

If you're flying, are they abroad? Something very English? Or something to remind them of their old home/area?

Or tea towels? (The lovely Irish linen ones; Ulster Weavers - I think they're made in Northern Ireland.) So many gorgeous designs and made in the UK. Very easy to pack!

I may be unimaginative, but I usually take something unbreakable such as table linen. I try to find something reminiscent of the area I live in although tea-towels maybe are too ordinary! I do sometimes give them with something else as my little city has lovely ones! I also give tea if it is permitted past customs. Although breakable, I have given teapots to some people who love English round ones.

I hate to tell you that the Ulster Weavers linen teatowels are no longer made in Northern Ireland but China... and sadly the linen is grown there too. I followed this up a few years ago as had bought a batch when they reappeared after an absence. On close examination the label on the town says made in China but the cardboard info tag has 'by appointment to her maj etc" Apparantly they are still designed in Northern Ireland hence can make that claim. The designs were as lovely as old ones but quality definitely inferior. Only place I have seen decent 100% linen is Australia by firm Rodriquez.

Thanks for this, HazelGreen. I didn't know about Ulster Weavers. Oh dear, another disappointment; it seems almost impossible to buy British-made gifts any more.

Depending where you are from, I’d take something hand-woven from your local area, maybe a throw or cushion cover - or some Irish linen as suggested above. Maybe pure linen glass towels or napkins.
My recent purchase was from Thomas Ferguson- but you can find others through the guild:
irishlinen.co.uk/

Dishtowels? how terribly unromantic.
Something fun and frivolous would be far better and they'd remember you.
If you don't like my hedgehog then some music they can both enjoy.
Though no one except me plays their own music these days . It's all streamed. LPs are supposed to be coming back....
I gave someone an old map of their area for a HW present. They were thrilled. It was so pretty. You can get them online from
www.oldmapsonline.org/

www.oldmap.co.uk/
maybe a better one