If your tent is reasonably tight then you might try to add some dehumidifying agent. Around where I live you can get those cheaply and they slowly absorb up to 500 ml from the ambient air. This might be enough to prevent condensation on your bike. The tighter and smaller the tent the better.
The question arose whether the desiccant would be sufficient in damp UK winter. The answer is yes. One cubic meter of air contains about 8g of water when fully saturated at 8°C. Assuming rather spacious 5 m³ for the tent, the 500ml dehumidifying container would be able to remove the entire moisture from the air about 12 times. This number drops to about 3.5 when we put the bike into the tent at 30°C in fully saturated air. We should also keep in mind that desiccant will usually not remove all moisture from ambient air (and that is not required to prevent rust). So even with significant leakage in the tent one simple dehumidifying container capable of absorbing 500ml of water from the air should be sufficient.
If worried about too much ingress of fresh moisture into the bike tent, then one can easily check the filling of the desiccant after a week. After initial removal of most moisture (including water drops left on the bike) the ingress of fresh moisture through leaks of the bike tent should be fairly constant, so that extrapolation should be feasible.
Additional benefit of this method: It potentially protects all components susceptible to rust, not just the oiled chain and related components. I had screws on my handle bar starting to rust during the first rainy season (continued to ride the bike through the rain and not much option to dry it).