I am not an arachnophobe, however my guest is..... this is their advice based on what I just did.
Do NOT say "Oh, I think something just fell into my hood"
Do NOT say "Oh! Its a spider!"
Do NOT say "Ooh thats a big bugger"
Do NOT put your hood up in order to grab said spider within the hood.
Do NOT then proceed to hold the hoodie enrobed spider in your hand whilst removing the hoodie.
Do NOT shake out hoodie in the garden.
DO call 999 to ask the fire service to attend
DO set your house on fire.
Thats was an interesting (and quite screamy) 5 minutes in my house!