According to its General Conditions of Carriage (which are fairly standard, and comply with EU261), British Airways should refund your money. This is a force majeure situation, so they aren't obligated to transport you from Newcastle to London, but they can't arbitrarily change your origin point and expect to keep your money, either. The EU has mandated that airlines must pay out refunds, as has the US Department of Transportation.
BA is in crisis on account of the collapse in travel demand triggered by the COVID-19 outbreak. Like other carriers, they are doing whatever they can to conserve cash and avoid a total collapse, and have been for weeks; that includes denying or delaying refunds. At this point, the risk of regulator sanctions or customer lawsuits or angry Tweets are irrelevant compared to surviving for another week, and BA has been one of the more conspicuously bad actors in this, as widely reported. Your options are limited.
Call the airline.
According to their Coronavirus travel and service updates page, and as also reported anecdotally, for a refund, you will need to get an agent on the phone and press them on the matter. It may be very difficult to get an agent on the phone, but if they have shut down operations at the airport there is no point in going there (which might also violate any orders against non-essential travel). If you have frequent flyer elite status, work those channels first.
Make an insurance claim.
Depending on when you bought your ticket and what is stated in the policy, you may qualify for compensation for trip interruption from your travel insurance provider, and you should contact the insurance company to file a claim. It isn't easy to may your insurance company pay even in good times, so this will also take an investment of time. If you didn't buy travel insurance, well, that's that.
File a chargeback.
You can also contact your credit card company and attempt a chargeback. Given the volume of people attempting to do this, the credit card issuer may also push back.
If you're willing to cancel the whole trip and accept a voucher for future travel, that option should still be available through BA's website, but I fully sympathize with a lack of faith in BA.