Hello...

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If you remove the island you will have more space but you lose counter space and storage. Its a flip. What do you need the most? Do you do lots of cooking for family events that you would need more prep room? If not remove it. you could add a small island or butcher block like McClure suggested that could solve the issue. What are your plans for the remodel? You could also change it up to add more storage options if that is what you are looking for.

It really just depends on how much you rely on the island ( storage, preparing ). One option might be to keep the island but have it on casters so that you can keep it out of the way until you need it. I would think twice before eliminating it you might miss it more than you think.

If you can use it and have someone walk behind you comfortably, keep it. I agree you'll miss the space it offers. If it is in the way remove it and reassess how you use the rest of the kitchen so you can reorgainze.

Another thought to consider, is there flooring under the island? If not, you'll need extra flooring to thread in.

I agree with Julie, you should definitely make sure there is flooring under it. By looking at the pictures, it looks like that flooring was installed later on at some point and is not going under the cabinets.
With that said, IMO you don't have much working counter space, and it looks like you have sufficient amount of room around it to move around it.
I know for a fact you want to have as much counter space as possible, especially working counter space, because that will be used at all times, not only for food prep, but everything else. When going to look at the kitchen remodeling job, first thing customer asks if there is room for an island.... no matter how small the kitchen is, customers always try to find space to stick an Island in it.
So if you fortunate enough to have one there and you have room to move around, leave it, you will not gain anything by removing it.

Islands are great IF you have enough room. One way to get more cabinet space is to go with 42" wall cabinets.