As Lloydsgiftstore has already pointed out, Royal Mail is usually offline during the evening at weekends but should be back online shortly. If, however, you are still experiencing issues with Royal Mail's website after the weekend then the other option would be to make a trip to your nearest Royal Mail branch in person and purchase the postage labels there.
In the meantime if you are worried about the delays impacting your customers perhaps it would be worth sending your buyers an e-mail via eBay Messages explaining the situation, stating that you will send them a further update as soon as the matter has been resolved. Once you have purchased the postage labels, whether online or in person, add each tracking number against the item it relates to and send each buyer a quick update to let them know that their items have now been despatched and that they ought to be receiving them shortly. Even if Royal Mail are experiencing problems it may well earn you a higher star rating with regards to seller communication when your buyers come to leave feedback for you, as the messages will be proof that you've done your best to keep your buyers updated regarding any problems, as opposed to keeping them in the dark and wondering what the hell is going on.