Future price == strike price in the future contract?

No great mystery here. You're absolutely correct, the value of this Future is now negative. The reason that you don't see Futures for sale at negative prices is that they have no value. It's the same with an Option which is out of the money, the option is now worthless and the holder will just let it expire. To attempt to sell it would be foolish, as no-one will buy it.

The missing link in the chain is that futures contracts do not specify the price that the owner of the contract will pay for the underlying asset. The price of the contract itself is how much its owner pays for delivery of the asset.

Following your example, the contract would be to deliver 1 tonne of corn on a certain date. The price you pay to buy the contract is how much you'll spend in total to have that 1 tonne of corn delivered to you on the expiry date.

So, to guarantee that you'll pay exactly $100 for 1 tonne of corn, you would buy 1 contract when it trades at $100. The contract writer gets $100 and you pay nothing on the expiration date to take delivery. In essence, you paid for the corn up front. If the price of corn goes down to $90 on the expiration date, the price of the futures contract would also be $90.

A future contract is essentially a non-optional call option.

I can see why you might think this, but is not accurate. I recommend you do not retain this mental model.

Therefore, the market value of this contract, right before the last trading second, is supposed to be £-10

No, the value is 90. The price of the contract is 90. Your PnL, is -10.

But things like this never happen - future contracts never have negative prices.

Futures contracts, and indeed many commodities and other assets and contracts can and do have negative prices. My garbage has a negative price to me, as I pay someone to take it from me.