Preheat the oven to 180C on fan mode. Cook spaghetti in a large saucepan of boiling, salted water, following packet directions, until al dente. Add peas to the pan for the last 2 minutes of cooking. Drain.
In a saucepan, pour some olive oil and fry bacon, until cooked but not crispy. Cut into small cubes and leave it aside. In the same pan cook mushrooms until golden.
Melt butter in a medium saucepan over medium-high heat. Add flour. Cook, stirring, for 1 minute or until bubbling and then gradually stir in milk. Bring to the boil. Reduce heat to medium.Cook, stirring, for 2 minutes or until mixture thickens. Remove pan from heat. Stir in 1/2 cup cheddar and half the chives. Season with salt and pepper.
Add pasta and peas to sauce. Stir to coat. Spoon mixture into a baking dish. Sprinkle with bacon and mushrooms and then the remaining cheddar and chives Bake for 25 to 30 minutes or until golden. Stand for 5 minutes. Serve.