Accesskey support changes depending on the markup and the browser. Pay attention to the environment and make sure you assign the accesskeys in the right way. Usage of accesskeys can aid a lot the navigation making your site much more usable.

On the UP.Browser, if you implement menus with the <select>/<option> construct, the browser will automatically create keyboard accelerators for your menus.

In the following example, keys 1 through 8 are the keyboard accelerator which allows direct jumps to each of the anchors.

<p><a accesskey="1" href="http://wfaq.net/links.php3">WAP Links</a></p>
<p><a accesskey="2" href="http://wfaq.net/demos.php3">WAP Demos</a></p>
...
<p><a accesskey="8" href="http://wfaq.net/email.php3">E-Mail</a></p>

The “accesskey” attribute has become standard in WAP 1.2.

You are now allowed to create links or lists of links with an accesskey associated. Using accesskeys is specifically suggested for links that often appear in a page such as “go to the Homepage” or “back”. If you always assign the same key, it will be automatic for the user to know that pressing that key will bring him back to the homepage.

Unfortunately, for some reason, some gateways will not like WML 1.2’s DTD and you might experience errors on the device. Unless you can test the accesskey support on the devices you target, the usage is discouraged for compatibility reasons.

Read more: What is the difference between WAP 1.1 and WAP 1.2?

The “accesskey” attribute is still present in XHTML-MP, so you can keep using it.

Luckily, from the WML 1.2 time, the support has greatly improved. Most browsers should support it without any problems.

The usage of accesskeys is STRONGLY suggested.

Read more: Can I set accesskey values in XHTML?

From the XHTML Basic Recommendation:
The XHTML Basic document type includes the minimal set of modules required to be an XHTML host language document type, and in addition it includes images, forms, basic tables, and object support. It is designed for Web clients that do not support the full set of XHTML features; for example, Web clients such as mobile phones, PDAs, pagers, and settop boxes. The document type is rich enough for content authoring. XHTML Basic is designed as a common base that may be extended. For example, an event module that is more generic than the traditional HTML 4 event system could be added or it could be extended by additional modules from XHTML Modularization such as the Scripting Module. The goal of XHTML Basic is to serve as a common language supported by various kinds of user agents. The document type definition is implemented using XHTML modules as defined in “Modularization of XHTML” [ XHTMLMOD ].

In chapter 3 of the XHTML Basic Recommendation, there’s a list of the modules that are part of it. The Hypertext Module includes the a element and accesskey is an attribute.
This confirms that accesskeys are supported in XHTML Basic.

XHTML Basic 1.1 is further step ahead, it includes accesskeys, of course, and other tags and attributes that are part XHTML-MP.
As of November 2006, XHTML Basic 1.1 is still not a recommendation.