Can anybody tell me what these spikes are growing out of our palm trees. They eventually open out into white fluffy looking balls then drop all over our garden.

I asked a gardener to remove them as when they open they attract wasps and I'm allergic to wasp sting. The garden dr told me that they could not cut them out until they opened as they would just grow more of these spikes.

I live near Alicante Spain 

Inflorescences

Yes, Washingtonia palms produce TONS of seeds!  What you're seeing is the beginning of the process...

Welcome to PalmTalk!  Please post more pictures of palms in or near Torrevieja!

But can I get them cut out now or will they grow again this year?

Well it depends if you want 10000 seeds or not. I’m assuming you don’t , so probably get them cut now. Otherwise later you’ll have to climb to cut them and also do a bunch of weeding palm seedlings below. 

Please though, if you decide to cut the flower stalks off, cut only that and nothing else. Your palm looks pretty trimmed already in terms of leaves and I wouldn’t be surprised if anyone you hire would mindlessly butcher your palm and leave it with 5 fronds. 

A healthy palm like yours will send up flower spikes every year no matter how many you cut off.  Wasp stings make me very sick so I look for the nest and destroy it to keep the numbers down. Bees and other beneficial insects like the flowers so I leave them on for them.

Peachy

Thanks, but what I really want to know is if I cut them off now will they grow again this year?

7 hours ago, anth said:

Thanks, but what I really want to know is if I cut them off now will they grow again this year?

It's possible - if they just started emerging yesterday there's a good likelihood that you'll get more.

They look pretty long already so that means they’re well developed flower stems. So you could cut them now. They might grow another set later in the year. The truth is you’ll always have to cut those, regardless of whether new ones grow or not, that’s a yearly task you just have to take on.