In general, all fixed appliances are supposed to be on their own circuit.
Thus, by code, you can't have something else on the same circuit as a washing machine. You can check your local building codes but I'll bet that's what they say.
Update
Technically the two minimum kitchen, pantry, dining room, breakfast room, or similar area, small appliance branch circuit only applies to outlets served on the walls, counter-tops, and/or floor outlets if they are within 18" of a wall. All other appliances, with the exception of refrigerators, that are fastened in place, CANNOT be included on the two minimum small appliance circuits. They MUST be on their own appliance circuit.
Still though, you may be able to combine and share the dishwasher and disposal on one dedicated circuit if the following conditions are met.
- The disposal is under 1HP
- The dishwasher is fastened in place.
- Lighting loads are not shared with the dishwasher/disposal.
- The manufacturer does not call for a dedicated circuit.
References
NEC 2014
210.23 Permissible Loads, Multiple-Outlet Branch Circuits
(A) (2) Utilization Equipment Fastened in Place. The total rating of utilization equipment fastened in place, other than luminaires, shall not exceed 50 percent of the branch-circuit ampere rating where lighting units, cord-and-plug-connected utilization equipment not fastened in place, or both, are also supplied.
430.53 Several Motors or Loads on One Branch Circuit
Two or more motors or one or more motors and other loads shall be permitted to be connected to the same branch circuit under conditions specified in 430.53( D) and in 430.53( A), (B), or (C). The branch-circuit protective device shall be fuses or inverse time circuit breakers.
(A) Not Over 1 Horsepower. Several motors, each not exceeding 1 hp in rating, shall be permitted on a nominal 120-volt branch circuit protected at not over 20 amperes or a branch circuit of 1000 volts, nominal, or less, protected at not over 15 amperes, if all of the following conditions are met:
The full-load rating of each motor does not exceed 6 amperes.
The rating of the branch-circuit short-circuit and ground-fault protective device marked on any of the controllers is not exceeded.
Individual overload protection conforms to 430.32.
Best Answer
It's only necessary that electric stoves (ovens in the UK) have their own circuit. This is because they draw more current (30A in the UK) than a lighting or power circuit.
It's OK to have a gas oven plugged into a normal mains circuit as they only use electricity for:
None of these are heavy load, so can be safely accommodated on a standard circuit.
The same rules about not overloading a circuit apply of course, so check what else is on this one as well as the cooker.