Booking.com told me Air China canceled my flight

This is tricky situation.

It's hard to tell without knowing what exactly happened at the airport, but the clock is ticking, so here is a "quick and dirty" answer.

1. You need to find out what the status of your ticket is and what exactly it says. If Air China is not answering the phone, try: http://www.airchina.com.cn/en/service/ticket-validating/ticket_validating.shtml
2. If that doesn't work try an online check in using your PNR (6 digit Passenger Name Record or Booking Reference) and see what happens
3. Keep good records of everybody you talked to: date, location, name. Especially of what happened at the airport.
4. Document the reason why you didn't fly: "ticket not valid", "wrong/date time", "check-in denied" etc.

Can I get a reimburs*m*nt for that?

Not really. No airline will cover "collateral damage" of a delayed or missed flight. Travel insurance might, but that depends on the specifics of the insurance and the exact reason why you didn't travel.

Can I get a refund or another flight tickets at this point?

It's unlikely (but not impossible) that you can change the ticket. You already tried that and it made a horrible mess. Refund is possible but that depends on the exact reasons of why didn't took your flight. If Air China did indeed changed you flight to what you posted than you are entitled to a refund since that itinerary is "unflyable". However, there are typically rules how to go about it including time windows. You really waited too long to deal with this.

Stating the obvious here: booking with a 3rd party instead of the airline directly is a really bad idea since you end up in customer service limbo. Waiting until the last minute to sort this out was also a bad idea.

As your flight departs from the UK, you are covered by the so-called UK261 rules, which are for now the same as the EU’s EC261.

When a flight is cancelled or substantially modified, you must be given the choice between rerouting and a refund.

Airlines will usually automatically suggest a new itinerary, but you have no obligation to accept it. You can ask it to be changed further (and since this is the airline’s fault, without any fees or penalties of course). They have an obligation to provide the earliest alternative available, even if it is on another airline or in a higher service class. If there is a seat available, they have to let you take it.

The problem is that going via a travel agent complicated things a lot. You can still try to contact the airline directly (even if the local office is closed, there must be a 24x7 line somewhere). At the airport there is often a ticketing desk, and you can always ask to talk to the airline’s station manager which should be available at any time there are flights about to depart. They were able to change your flights unilaterally without the travel agent, they can do it again. Ultimately, they are the ones on the hook to refund and possibly compensate you, so they have every reason to accommodate you (especially since this is their fault).

If you opt for a refund, since you were notified less than 14 days before the flight, you are also eligible for compensation, whatever the GBP equivalent of 600 euros is.

Under that regime, you wouldn’t be able to get more. If the cost to you was higher, the best option is to use your travel insurance (even if you don’t have subscribed for one explicitly, you could have travel insurance bundled with your credit card or other contracts). Other than that, you can try to claim for damages in court, but it’s likely they will be capped by the Montreal Convention.

Note that the UK261 protection will only apply for your outbound flight. The inbound flight is not covered.